**Particle Filter Based State Estimation: Not Always a Mean Thing**

*Time:* 13:15-14:00. *Place:* Glashuset.

The Particle Filter (PF) or sequential Monte Carlo filter is becoming one of the standard tools in a multitude of fields, such as radar processing, air traffic control, navigation and finance, just to name a few. More and more applications appear for which the PF illustrates enhanced performance over classical methods. One of the major advantages of this filter is that it allows the user to implement the exact Bayesian solution, with the only approximation being in the finite number of particles used. Another important and practically very relevant issue is how to represent the output of the PF to a user. Straightforward and naive presentation of the mean of the cloud as a point estimate may lead to dramatically (bad) results and plainly wrong conclusions in a multi object setting as well as in some other applications. We will adress the underlying problem for this. Furthermore, we will provide new and efficient methods for Maximum A Posteriori (MAP) state estimation, based on a running particle filter. We will adress convergence issues of these approximate particle based MAP estimators. Furthermore, the power of the MAP method will be illustrated through some relevant examples.

**Efficient Estimation and Detection Methods for Airborne Applications**

*Time:* 10:00-12:00. *Place:* Visionen.

The overall purpose with this thesis is to investigate and provide computationally efficient methods for estimation and detection. The focus is on airborne applications, and we seek estimation and detection methods which are accurate and reliable yet effective with respect to computational load. In particular, the methods shall be optimized for terrainaided navigation and collision avoidance respectively. The estimation part focuses on particle filtering and the in general much more efficient marginalized particle filter. The detection part focuses on finding efficient methods for evaluating the probability of extreme values. This is achieved by considering the, in general, much easier task to compute the probability of level-crossings.

The concept of aircraft navigation using terrain height information is attractive because of the independence of external information sources. Typically terrain-aided navigation consists of an inertial navigation unit supported by position estimates from a terrain-aided positioning (TAP) system. TAP integrated with an inertial navigation system is challenging due to its highly nonlinear nature. Today, the particle filter is an accepted method for estimation of more or less nonlinear systems. At least when the requirements on computational load are not rigorous. In many on-line processing applications the requirements are such that they prevent the use of the particle filter. We need more efficient estimation methods to overcome this issue, and the marginalized particle filter constitutes a possible solution. The basic principle for the marginalized particle filter is to utilize linear and discrete substructures within the overall nonlinear system. These substructures are used for efficient estimation by applying optimal filters such as the Kalman filter. The computationally demanding particle filter can then be concentrated on a smaller part of the estimation problem.

The concept of an aircraft collision avoidance system is to assist or ultimately replace the pilot in order to to minimize the resulting collision risk. Detection is needed in aircraft collision avoidance because of the stochastic nature of the sensor readings, here we use information from video cameras. Conflict is declared if the minimum distance between two aircraft is less than a level. The level is given by the radius of a safety sphere surrounding the aircraft. We use the fact that the probability of conflict, for the process studied here, is identical to the probability for a down-crossing of the surface of the sphere. In general, it is easier to compute the probability of down-crossings compared to extremes. The Monte Carlo method provides a way forward to compute the probability of conflict. However, to provide a computationally tractable solution we approximate the crossing of the safety sphere with the crossing of a circular disc. The approximate method yields a result which is as accurate as the Monte Carlo method but the computational load is decreased significantly.

**Modeling energy systems - examples in a systems perspective**

*Time:* 13:15-14:00. *Place:* Glashuset.

At the division Energy systems at IEI different energy systems are analyzed, ranging from buildings, industries and regional/local energy systems. The analyses are mainly carried through by using some kind of computer software tool, based on optimization routines or simulation mathematics. At this presentation one of these tools will shortly be described and thereafter a couple of examples on energy systems modeling will be presented briefly. System aspects will be the focus during the presentation.

**Complexity Issues, Validation and Input Design for Control in System Identification**

*Time:* 13:15-14:00. *Place:* Glashuset.

This seminar is a summary of Dr. Märta Barenthin Syberg's Ph.D. project.

System identification is about constructing and validating models from measured data. When designing system identification experiments in control applications, there are many aspects to consider. One important aspect is the choice of model structure. Another crucial issue is the design of input signals. Once a model of the system has been estimated, it is essential to validate the closed loop performance if the feedback controller is based on this model. In this thesis we consider the prediction-error identification method. We study model structure complexity issues, input design and model validation for control.

To describe real-life systems with high accuracy, models of very high complexity are typically needed. However, the variance of the model estimate usually increases with the model order. In this presentation we investigate why system identification, despite this rather pessimistic observation, is successfully applied in the industrial practise as a reliable modelling tool. It is shown that by designing suitable input signals for the identification experiment, we obtain accurate estimates of the frequency function also for very complex systems. The input power spectrum can be used to shape the model quality. A key tool in input design is to introduce a linear parametrization of the spectrum. With this parametrization, several optimal input design problems can be rewritten as convex optimization problems.

Another problem considered is to design controllers with guaranteed robust stability and prescribed robust performance using models identified from experimental data. These models are uncertain due to process noise, measurement noise and unmodelled dynamics. In this presentation we only consider errors due to measurement noise. The model uncertainty is represented by ellipsoidal confidence regions in the model parameter space. We develop tools to cope with these ellipsoids for scalar and multivariable models. These tools are used for designing robust controllers, for validating the closed loop performance and for improving the model with input design. Therefore this project is part of the research effort to connect prediction-error identification methods and robust control theory.

**Convex relaxations with applications to robust control problems**

*Time:* 13:15-14:00. *Place:* Glashuset.

It is a known fact that many relevant challenges in robust control boil down to the solution of non-convex optimization problems. Since in the last decades a lot of progresses in the solution of convex problems have been made, researchers in the robust control field have devoted their attention to the development of convex relaxations of non-convex problems. In this talk, two different kind of non-convex problems are introduced together with their relaxations.

In the first part, I will recall the quadratic distance problem (QDP), an important family of problems that are relevant to the control field, and I will present some of the convex relaxations for QDPs which are based on the sum-of-squares representation of positive polynomials. I will show the obtained results about the relationships in terms of conservatism among the different relaxations.

In the second part, I will introduce the exploitation of convex relaxations for the robust stability analysis of uncertain systems in linear fractional representation (LFR), with particular application to LFR systems derived from the real-world flight control schemes within the EU project COFCLUO. The considered relaxations are based on the Lyapunov stability theory, a widely used tool to assess robust stability of dynamic systems affected by parametric uncertainties. Since it is know that, when the uncertain parameters are constant or slowly time-varying, parameter-dependent Lyapunov functions allow one to reduce conservatism of sufficient conditions for robust stability, several different convex relaxations based on parameter-dependent Lyapunov functions have been taken into account. Such techniques have been applied to LFR systems delivered within COFCLUO, with the aim of finding the largest region in the uncertain parameter space for which robust stability is guaranteed. I will present and discuss the preliminary results obtained from this analysis.

**Optimal placement of communications relay nodes**

*Time:* 13:15-14:00. *Place:* Visionen (MOVIII seminar).

We consider a constrained optimization problem with mixed integer and real variables. It models optimal placement of communications relay nodes. This problem is widely encountered for instance, in robotics, where it is required to survey some target located in one point and convey the gathered information back to a base station located in another point. One or more inmanned aerial or ground behicles (UAVs or UGVs) can be used for this purpose as communication relays. The number of unmanned vehicles (UVs) is the only integer among the decision variables. The positions of UVs specified by real variables are assessed by a merit function, and the sum of the function values is to be minimized. We suggest to use an obstructed volume as a merit function, whose value is determined by the UV position and the local terrain around it. The relay of UVs are required to be placed in the area of interest subject to the following requirements. Firstly, the line segment connecting any consecutive pair of UVs, the base and the first UV, as well as the last UV and the target, should not intersect with the obstacles (a free line of sight requirement). Secondly, the distance between these pairs should not exceed a given limit defined by the communication range. Because of these requirements, our constrained optimization problem is a difficult multi-extremal problem for any fixed number of UVs. Moreover, the feasible set of real variables is typically disjoint. We present an approach that allows us to efficiently find a reasonably accurate approximation to a global minimum in the problem of optimal placement of communications relay nodes. It is based on a spatial discretization with a subsequent reduction to the shortest path problem.

The case of a restricted number of available UVs is also considered here. We introduce two label correcting algorithms which are able to take advantage of using some peculiarities of the resulting restricted shortest path problem. The algorithms produce a Pareto solution to the two-objective problem of minimizing the path cost and the number of hops. We prove the correctness of these algorithms. The presented results of numerical 3D experiments show that our algorithms are superior to the conventional Bellman-Ford algorithm tailored to solving this problem.

**Distributed Optimization in Networked Systems - Why? How? Does it work in practice?**

*Time:* 13:15-14:00. *Place:* Glashuset.

Many systems consist of cooperating subsystems that are connected through a network, and several important tasks in such systems can be posed as optimization problems. To improve scalability and resilience against individual subsystem failure, it can be useful to use distributed algorithms to solve these optimization problems. In this talk, I'll give some motivating examples where distributed optimization is useful. I will also describe two novel decentralized optimization algorithms that are tailored to be used in networked systems. The key feature of both algorithms is that they only need neighbor-to-neighbor communication to solve the optimization problem. Finally, I'll present experimental results from our implementation of different optimization algorithms on a wireless sensor network.

**On low order controller synthesis using rational constraints**

*Time:* 10:15-12:00. *Place:* Visionen.

In order to design robust controllers, H-infinity synthesis is a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the plant, the problem is no longer convex and it is then relatively hard to solve. These problems become very complex, even when the order of the system to be controlled is low.

The approach used in the thesis is based on formulating the constraint on the maximum order of the plant as a polynomial equation. By using the fact that the polynomial is non-negative on the feasible set, the problem is reformulated as an optimization problem where the nonconvex polynomial function is to be minimized over a convex set defined by linear matrix inequalities.

To solve this optimization problem, two methods have been proposed. The first method is a barrier method and the second one is a method based on a primal-dual framework. These methods have been evaluated on several problems and compared with a well-known method found in the literature. To motivate this choice of method, we have made a brief survey of available methods available for solving the same or related problems.

The proposed methods emerged as the best methods among the three for finding lower order controllers with the same or similar performance as the full order controller. When the aim is to find the lowest order controller with no worse than +50% increase in the closed loop H-infinity norm, then the three compared methods perform equally well.

**On the Behavior of the Conjugate-Gradient Method on Ill-Conditioned Problems**

*Time:* 13:15-14:00. *Place:* Glashuset.

The conjugate-gradient method is a well-known iterative method for minimizing a quadratic function where the Hessian is positive definite. In this talk, we discuss some aspect of the method that may be less well known. In particular, we study the behavior of the conjugate-gradient method on ill-conditioned problems, for which the Hessian has one set of eigenvalues that are large and the remaining are small. Our motivation is twofold: first, interior methods, where infinitely ill-conditioned matrices arise, and second, radiation therapy optimization, where ill-conditioned systems arising from discretized Fredholm equations of the first kind arise. We characterize the behavior of the residuals associated with the large eigenvalues throughout the iterations, and also characterize the behavior of the residuals associated with the small eigenvalues for the early iterations. Our results show that the residuals associated with the large eigenvalues are made small first, without changing very much the residuals associated with the small eigenvalues. Subsequently, the residuals associated with the small eigenvalues are reduced.

The motivation for this research comes from radiation therapy optimization.

**Docentföreläsning: Using parametric optimization in system identification and regression**

*Time:* 13:15-14:00. *Place:* Glashuset.

When encountering an optimization problem where two or more objective functions should be optimized simultaneously, one can formulate the problem as a parametric optimization problem. Often, the objective functions are more or less contradictory, which means that some trade-off has to be made. If there is an efficient way of computing the solution for all possible trade-off choices, this is an advantage, since the final choice can then be made afterwards by comparing the different solutions.

System identification is about modelling dynamic systems from experimental measurement data, and has a wide area of applications ranging from, e.g., automotive industry to systems biology. A classical trade-off in system identification is between minimizing bias and variance. When the model structure and noise variance are partially unknown, this can be viewed as a parametric optimization problem. A related problem occurs in regularized regression, where in for instance the LASSO method there is a trade-off between fitting the model well to data and model complexity.

In this lecture, we will look at the LASSO method and a certain system identification method called Direct Weight Optimization (DWO), and how parametric optimization can be used to compute the solutions for all trade-offs simultaneously. The final choice can then be made, e.g., via cross-validation.

**Sensor placement analysis for fault isolation**

*Time:* 13:15-14:00. *Place:* Glashuset.

This presentation will outline procedures for computing which sensors that are needed to meet a given diagnosis requirement specification with respect to fault detectability and fault isolability.

First, linear differential-algebraic models will be considered and then the approach is extended, using so called structural analysis, to cover large non-linear differential-algebraic models. The algorithms have completeness properties in the sense that they compute a characterization of all solutions that fulfill the requirements. For cases where the requirements are unattainable, maximizing solutions are computed. The approach is exemplified on a number of examples, ranging from small electrical circuits to larger models of gas turbines and drivelines in hybrid vehicles.

**Global Robust Stabilization and Output Regulation by State Feedback for Feedforward Systems and Their Applications**

*Time:* 13:15-14:00. *Place:* Glashuset.

The control of nonlinear systems has been one of the major subjects in control theory. Due to the complexity of nonlinear systems, there is no general approach for the control of nonlinear systems. Instead, there are a lot of approaches, each of which is best applicable for a particular class of nonlinear systems. Since the 1990s, some recursive design approaches have been suggested for two important classes of nonlinear systems, namely, systems in feedback form and systems in feedforward form. While the research on the first class of systems has reached a certain degree of maturity, the research on the second class of systems is still in its infancy. In this talk, the research on the stabilization and output regulation problems of feedforward systems will be introduced. Accordingly, this talk contains two parts. The first part studies the global robust stabilization problem of feedforward systems and the second part further addresses the global robust output regulation problem of the feedforward system.

The stabilization problem of feedforward systems has absorbed a lot of attention during the past fifteen years. More recently, the stabilization problem of feedforward systems subject to input unmodeled dynamics is studied. Nevertheless, the more realistic case where the system is subject to both static uncertainty and dynamic uncertainty has not been adequately investigated. The first part of this talk focuses on the global robust stabilization problem for various classes of feedforward systems containing both static uncertainty and dynamic uncertainty. On the other hand, it is now well known from the general framework for tackling the output regulation problem that the robust output regulation problem can be approached in two steps. In the first step, the problem is converted into a robust stabilization problem of a so-called augmented system which consists of the original plant and a suitably defined dynamic system called an internal model candidate, and in the second step, the robust stabilization problem of the augmented system is further pursued. The success of the first step depends on whether or not an internal model candidate exists. Even though the first step succeeds, the success of the second step is by no means guaranteed due to at least two obstacles. First, the stabilizability of the augmented system is dictated not only by the given plant but also by the particular internal model candidate employed. Second, the stabilization problem of the augmented system is much more challenging than that of the original plant with the exogenous signal set to 0, because the structure of the augmented system may be much more complex than that of the original plant. Perhaps, it is because of these difficulties, so far almost all papers on semi-global or global robust output regulation problem are focused on the lower triangular systems, feedback linearizable systems and output feedback systems. The second part of this talk aims to study the global robust output regulation problem of feedforward systems. For application, we apply the result of the global robust output regulation problem to solve the trajectory tracking problem for a chain of integrators with uncertain parameters and Vertical Take-Off and Landing (VTOL) aircraft, respectively. In contrast with the existing designs, for the chain of integrators, our design does not need to know the reference trajectory exactly, and for the VTOL aircraft, our design is low-gain and thus is more cost effective and more suitable for practical implementation.

The major approach in this talk is the small gain approach. In particular, a small gain based bottom-up recursive design procedure is proposed to deal with the stabilization problem for various classes of feedforward systems. Two types of the small gain theorem with restrictions adapted from [A nonlinear small gain theorem for the analysis of control systemswith saturation, IEEE-TAC, Teel, 1996] is applied to establish the local stability and global attractiveness of the closed-loop system at the origin respectively.

**Task planning and control of Semi-autonomous Surveillance UGVs**

*Time:* 13:15-14:00. *Place:* Glashuset.

This talk will cover two results from the AURES project (Autonomous UGV-systems for REconnaissance and Surveillance) which is part of the FMV-funded TAIS program (Technologies of Autonomous and Intelligent Systems).

The first result describes how feedback linearization can be used to enhance the user interface for teleoperation of tracked UGVs. By introducing an intermediate control layer, a user interface that is very similar to so-called first person shooter (FPS) computer games, e.g. Doom and Half Life, can be created. The advantages of such interfaces is that they are intuitive, and that literally millions of potential future UGV-operators already have spent hundreds of hours training with them. The control mode gives the user direct control of the position and orientation of the on-board camera, while the actual orientation of the vehicle is abstracted away using feedback linearization.

The second result deals with choosing positions for a group of UGVs such that the combined camera images can be used to carry out a given surveillance task. Two such tasks are considered. The first is to monitor all walls of a given set of buildings, while satisfying camera constraints in terms of range, field of view and resolution. The second task is to create a line-of-sight perimeter around a given set of buildings to keep track of anyone entering or leaving the area.

**MOVIII Seminar – What we don't know about Robotic Aircraft or UAS**

*Time:* 13:15-14:00. *Place:* Visionen.

The ARCAA has been conducting research in the area of robotic aircraft

(UAS, UAV, ..) since 1999. In this time the group has been on journey

of understanding, beginning with very little knowledge of the problems

associated with these vehicle, and looking from the elec eng/computer

science perspective. This talk will address the issues of societal

acceptance of UAS, followed by a discussion of current issues

associated with regulatory impediments. Specific comment will be made

in the Australian context. It will also highlight problems that remain

to be solved for UAS.

Research results will be provided for two research thrusts; namely the

emergency (or forced) landing problem and the "see and avoid" problem.

These areas being investigated for automation through the use of

computer vision techniques. A brief overview and video of our flight

test activities for the "Smart Skies" program (an automated aircraft

separation program) and our robotic powerline asset inspection program

will be provided. Finally, speculation of the future development path,

and likely hurdles, for robotic aircraft will be provided.

Biography:

Rod Walker is the Professor of Aerospace Avionics at the Queensland

University of Technology and the Director of the Australian Research

Centre for Aerospace Automation (ARCAA). ARCAA is a joint venture

between QUT and the CSIRO ICT Centre. In his career he been

responsible for the development of electromagnetic propagation models

(parabolic equation method) to estimate the performance of the GPS in

multipath significant environments. He was also the GPS program

leader on an Australia national satellite program "FedSat" working

closely with the NASA Jet Propulsion Lab to deliver and operate the

GPS payload. Over the last decade he has turned his attention to the

aviation environment and focuses on removing impediments to increasing

automation in this context. He is a private pilot with aerobatic

endorsement. He is on the board of AUVSI Australia and Chairs a

National Committee on UAS Regulatory Development. His group has over

30 staff and a custom built facility at Brisbane International

Airport.

**Probabilistic Techniques for Mobile Robot Navigation**

*Time:* 09:00-10:00. *Place:* Visionen.

In recent years, probabilistic techniques have enabled novel and innovative solutions to some of the most important problems in mobile robotics. Major challenges in the context of probabilistic algorithms for mobile robot navigation lie in the questions of how to deal with highly complex state estimation problems and how to control the robot so that it efficiently carries out its task. In this talk I will discuss both aspects and present an efficient probabilistic approach to solve the simultaneous mapping and localization problem for mobile robots. I will also describe how this approach can be combined with an exploration strategy that simultaneously takes into account the uncertainty in the pose of the robot and in themap. For all algorithms I will present experimental results, which have been obtained with mobile robots in real-world environments as well asin simulation. I will conclude the presentation with a discussion of open issues and potential directions for future research.

**Robots in manufacturing research at University West**

*Time:* 13:15-14:00. *Place:* Glashuset.

Research at University West in Trollhättan makes use of industrial robots as an important part of a manufacturing system. Our projects are mainly financed by the European Union, Vinnova and the KK-foundation. The seminar will present current and planned activities with focus on robots and control for manufacturing. These include:

- Welding and Metal deposition

- Machine Vision applications

- Coordinating robots

- Friction Stir Welding

- Off-Line Programming and Robot Simulation

Further University West offer a wide range of robotic/automation education for bachelor and master students.

Research and automation/robotic courses take place at Production Technology Centre in Trollhättan.

**Hardware Implementation of Model Predictive Control**

*Time:* 13:15-14:00. *Place:* Glashuset.

Model predictive control (MPC) is used extensively in industry. A key reason is that MPC offers better control performance in many practical situations. Of note is MPC's ability to handle system constraints such as valve limits or maximum pressure bounds. This ability comes at the expense of having to solve an optimization problem online. This has restricted the application of MPC to systems with relatively slow or simple dynamics. At the same time, there are a growing number of applications that require MPC to run at high speed, using low power, and on embedded hardware. Two examples of these typesof applications of MPC are discussed in the talk. A theme of the talk is to illustrate how the MPC algorithm can be implemented in FPGA or ASIC technologies.

Bio: Adrian Wills was born in Orange, N.S.W. Australia and received his B.E. (Elec.) and Ph.D. degrees from The University of Newcastle, Australia (Callaghan Campus) in May 1999 and May 2003, respectively. Since then he has held a postdoctoral research position at Newcastle, where the focus of his research has been in the areas of Model Predictive Control and System Identification. Details of his research activities are available at www.sigpromu.org/onyx.