The so-called nonlinear H∞-control problem in state space is considered with an emphasis on developing machinery with promising computational properties. Both state feedback and output feedback H∞-control problems for a class of nonlinear systems are characterized in terms of continuous positive definite solutions of algebraic nonlinear matrix inequalities which are convex feasibility problems. The issue of existence of solutions to these nonlinear matrix inequalities (NLMIs) is justified.

This paper gives an overview of promising new developments in robust stability and performance analysis of linear control systems with real parametric uncertainty. The goal is to develop a practical algorithm for medium size problems, where medium size means less than 100 real parameters, and "practical" means avoiding combinatoric (nonpolynomial) growth in computation with the number of parameters for all of the problems which arise in engineering applications. We present an algorithm and experimental evidence to suggest that this goal has, for the first time, been achieved. We also place these results in context by comparing with other approaches to robustness analysis and considering potential extensions, including controller synthesis. 1 Introduction Robust stability and performance analysis with real parametric uncertainty can be naturally formulated as a Structured Singular Value, or , problem, where the block structured uncertainty description is allowed to contain both...

This paper describes recent results on system design and implementation of Berkeley UAV. The system design deploys the architecture of a Flight Vehicle Management System, FVMS, which combines planning and control. The resulting hierarchical control strategy which involves the interaction of continuous dynamics and discrete events is a hybrid system. Three controller based on different control methodologies are designed for various types of man oeuvres and flight modes, and their performance are evaluated under simulation based on a nonlinear model. The FVMS interacts with a vision system which is responsible for detection and recognition of different types of hazardous waste barrels. The vision algorithm consists of three parts: filtering, segmentation, and recognition. A 3D virtual environment simulation , SmartAerobots, is developed as a visualization tool. A helicopter-based aerial vehicle has been constructed and the proposed algorithms are being implemented and verified. 1 Introdu...

Still the doctor — by a country mile! Preferences for health services in two country towns in north-west New South Wales he relative importance people place on particular healthcare services is a significant factor in meeting their healthcare needs and influencing their health behaviour.

OF DISSERTATION A SYNTHESIS OF REINFORCEMENT LEARNING AND ROBUST CONTROL THEORY The pursuit of control algorithms with improved performance drives the entire control research community as well as large parts of the mathematics, engineering, and artificial intelligence research communities. A fundamental limitation on achieving control performance is the conflicting requirement of maintaining system stability. In general, the more aggressive is the controller, the better the control performance but also the closer to system instability.

We apply the passivity theorem with appropriate choice of multipliers to develop sufficient conditions for stability of the general anti-windup bumpless transfer (AWBT) framework presented in [24]. For appropriate choices of the multipliers, we show that these tests can be performed using convex optimization over linear matrix inequalities (LMIs). We show that a number of previously reported attempts to analyze stability of AWBT control systems, using such well-known and seemingly diverse techniques as the Popov, Circle and Off-Axis Circle criteria, the optimally scaled small-gain theorem (generalized ¯ upper bound) and describing functions, are all special cases of the general conditions developed in this paper. The sufficient conditions are complemented by necessary conditions for internal stability of the AWBT compensated system. Using an example, we show how these tests can be used to analyze the stability properties of a typical anti-windup control scheme. 1 Introduction All real...

We consider robust semi-definite programs which depend polynomially or ratio-nally on some uncertain parameter that is only known to be contained in a set with a polyno-mial matrix inequality description. On the basis of matrix sum-of-squares decompositions, we suggest a systematic procedure to construct a family of linear matrix inequality relaxations for computing upper bounds on the optimal value of the corresponding robust counterpart. With a novel matrix-version of Putinar’s sum-of-squares representation for positive polynomials on compact semi-algebraic sets, we prove asymptotic exactness of the relaxation family under a suitable constraint qualification. If the uncertainty region is a compact polytope, we provide a new duality proof for the validity of Putinar’s constraint qualification with an a priori degree bound on the polynomial certificates. Finally, we point out the consequences of our results for constructing relaxations based on the so-called full-block S-procedure, which allows to apply recently developed tests in order to computationally verify the exactness of possibly small-sized relaxations.

. A fast algorithm for the computation of the optimally frequencydependent scaled H1-norm of a finite dimensional LTI system is presented. It is well known that this quantity is an upper bound to the "¯-norm"; furthermore, it was recently shown to play a special role in the context of slowly time-varying uncertainty. Numerical experimentation suggests that the algorithm generally converges quadratically. Keywords. Robust control, numerical methods, structured singular value, uncertain linear systems. 1. INTRODUCTION In the context of robust control analysis and synthesis a quantity of great interest is the structured singular value norm, or ¯-norm, of the system. Consider a feedback connection as in Figure 1. Let P (s) = C(sI \Gamma A) \Gamma1 B be an m \Theta m transfer function matrix and let \Delta(s) be a structured perturbation constrained to lie in the set R(\Delta) \Delta = f \Delta 2 RS : \Delta(s 0 ) 2 \Delta 8s 0 2 C+ g where RS is the set of all real-rational, proper,...

We study semi-infinite systems of Linear Matrix Inequalities which are generically NP-hard. For these systems, we introduce computationally tractable approximations and derive quantitative guarantees of their quality. As applications, we discuss the problem of maximizing a Hermitian quadratic form over the complex unit cube and the problem of bounding the complex structured singular value. With the help of our complex Matrix Cube Theorem we demonstrate that the standard scaling upper bound on µ(M) is a tight upper bound on the largest level of structured perturbations of the matrix M for which all perturbed matrices share a common Lyapunov certificate for the (discrete time) stability. 1

Abstract. In this paper we study the variation of the spectrum of block-diagonal systems under perturbations of compatible block structure with fixed zero blocks at arbitrarily prescribed locations (“Gershgorin-type perturbations”). We derive explicit and computable formulae for the associated μ-values. The results are then applied to characterize spectral value sets and stability radii for such perturbed systems. By specializing our results to the scalar diagonal case, the classical eigenvalue inclusion theorems of Gershgorin, Brauer, and Brualdi are obtained as corollaries. Moreover it follows that the inclusion regions of Brauer and Brualdi are optimal for the corresponding perturbation structures.