H? Gain Scheduling for Discrete-Time Systems with Control Delays and Time-Varying Parameters: a BMI Approach

In this paper, the problem of gain scheduling for time-varying systems with time delays is investigated. By using a memory at the feedback loop, a discrete gain scheduled controller which minimizes an upper bound to the ,Hscrinfin performance of the closed loop system is determined. The design conditions, expressed in terms of bilinear matrix inequalities, are obtained from the Finsler\u27s Lemma combined with the Lyapunov theory. The extra variables introduced by the Finsler\u27s Lemma represent an alternative way in the search of better system behavior. The time-varying uncertainties are modeled using polytopic domains. The controller is obtained by the solution of an optimization problem formulated only in terms of the vertices of the polytope. No grids in the parametric space are used. Numerical examples illustrate the efficiency of the proposed approach

Stabilization of uncertain linear systems: an LFT approach

This paper develops machinery for control of uncertain linear systems described in terms of linear fractional transformations (LFTs) on transform variables and uncertainty blocks with primary focus on stabilization and controller parameterization. This machinery directly generalizes familiar state-space techniques. The notation of Q-stability is defined as a natural type of robust stability, and output feedback stabilizability is characterized in terms of Q-stabilizability and Q-detectability which in turn are related to full information and full control problems. Computation is in terms of convex linear matrix inequalities (LMIs), the controllers have a separation structure, and the parameterization of all stabilizing controllers is characterized as an LFT on a stable, free parameter

Control and filtering of time-varying linear systems via parameter dependent Lyapunov functions

The main contribution of this dissertation is to propose conditions for linear filter and controller design, considering both robust and parameter dependent structures, for discrete time-varying systems. The controllers, or filters, are obtained through the solution of optimization problems, formulated in terms of bilinear matrix inequalities, using a method that alternates convex optimization problems described in terms of linear matrix inequalities. Both affine and multi-affine in different instants of time (path dependent) Lyapunov functions were used to obtain the design conditions, as well as extra variables introduced by the Finsler\u27s lemma. Design problems that take into account an H-infinity guaranteed cost were investigated, providing robustness with respect to unstructured uncertainties. Numerical simulations show the efficiency of the proposed methods in terms of H-infinity performance when compared with other strategies from the literature

A necessary and sufficient minimality condition for uncertain systems

A necessary and sufficient condition is given for the exact reduction of systems modeled by linear fractional transformations (LFTs) on structured operator sets. This condition is based on the existence of a rank-deficient solution to either of a pair of linear matrix inequalities which generalize Lyapunov equations; the notion of Gramians is thus also generalized to uncertain systems, as well as Kalman-like decomposition structures. A related minimality condition, the converse of the reducibility condition, may then be inferred from these results and the equivalence class of all minimal LFT realizations defined. These results comprise the first stage of a complete generalization of realization theory concepts to uncertain systems. Subsequent results, such as the definition of and rank tests on structured controllability and observability matrices are also given. The minimality results described are applicable to multidimensional system realizations as well as to uncertain systems; connections to formal powers series representations also exist

Fault-Tolerant Flight Control Using One Aerodynamic Control Surface

University of Minnesota Ph.D. dissertation. June 2018. Major: Aerospace Engineering and Mechanics. Advisor: Peter Seiler. 1 computer file (PDF); xiii, 291 pages.Small unmanned aircraft systems (UAS) have recently found increasing civilian and commercial applications. On-board fault management is one of several technical challenges facing their widespread use. The aerodynamic control surfaces of a fixed-wing UAS perform the safety-critical functions of stabilizing and controlling the aircraft. Failures in one or more of these surfaces, or the actuators controlling them, may be managed by repurposing the other control surfaces and/or propulsive devices. A natural question arises in this context: What is the minimum number of control surfaces required to adequately control a handicapped aircraft? The answer, in general, depends on the control surface layout of the aircraft under consideration. For some aircraft, however, the answer is one. If the UAS is equipped with only two control surfaces, such as the one considered in this thesis, then this limiting case is reached with a single control surface failure. This thesis demonstrates, via multiple flight tests, the autonomous landing of a UAS using only one aerodynamic control surface and the throttle. In seeking to arrive at these demonstrations, this thesis makes advances in the areas of model-based fault diagnosis and fault-tolerant control. Specifically, a new convex method is developed for synthesizing robust output estimators for continuous-time, uncertain, gridded, linear parameter-varying systems. This method is subsequently used to design the fault diagnosis algorithm. The detection time requirement of this algorithm is established using concepts from loss-of-control. The fault-tolerant controller is designed to operate the single control surface for lateral control and the throttle for total energy control. The fault diagnosis algorithm and the fault-tolerant controller are both designed using a model of the aircraft. This model is first developed using physics-based first-principles and then updated using system identification experiments. Since this aircraft does not have a rudder, the identification of the lateral-directional dynamics requires some novelty

Linear Matrix Inequality Approach to Robust Emergency Lateral Control of a Highway Vehicle With Time-Varying Uncertainties.

New linear-matrix-inequality (LMI) based methods are developed for the static-output-feedback stabilization and reduced-gain static-output-feedback stabilization of time-invariant systems. Unlike previous methods, the static-output-feedback method is non-iterative in LMI solutions. The methods are extended to design robust static-output-feedback controllers for time-varying systems using a polytopic-systems approach. Examples are given which demonstrate the use of each of the new methods. The specific problem of emergency lateral control of a highway vehicle is then addressed using the new robust static-output-feedback method. A controller is designed which robustly stabilizes the vehicle over the range of highway speeds (15 to 30 m/s) and a range of expected independent changes in front and rear lateral tire stiffness (15 to 30 kN/rad)

Systems and control : 21th Benelux meeting, 2002, March 19-21, Veldhoven, The Netherlands

Book of abstract

Discrete-time optimal preview control

There are many situations in which one can preview future reference signals, or future disturbances. Optimal Preview Control is concerned with designing controllers which use this preview to improve closed-loop performance. In this thesis a general preview control problem is presented which includes previewable disturbances, dynamic weighting functions, output feedback and nonpreviewable disturbances. It is then shown how a variety of problems may be cast as special cases of this general problem; of particular interest is the robust preview tracking problem and the problem of disturbance rejection with uncertainty in the previewed signal. . (', The general preview problem is solved in both the Fh and Beo settings. The H2 solution is a relatively straightforward extension ofpreviously known results, however, our contribution is to provide a single framework that may be used as a reference work when tackling a variety of preview problems. We also provide some new analysis concerning the maximum possible reduction in closed-loop H2 norm which accrues from the addition of preview action. / Name of candidate: Title of thesis: I DESCRIPTION OF THESIS Andrew Hazell Discrete-Time Optimal Preview Control The solution to the Hoo problem involves a completely new approach to Hoo preview control, in which the structure of the associated Riccati equation is exploited in order to find an efficient algorithm for computing the optimal controller. The problem tackled here is also more generic than those previously appearing in the literature. The above theory finds obvious applications in the design of controllers for autonomous vehicles, however, a particular class of nonlinearities found in typical vehicle models presents additional problems. The final chapters are concerned with a generic framework for implementing vehicle preview controllers, and also a'case study on preview control of a bicycle.Imperial Users onl