Resilient dynamic controller design via quadratic Lyapunov bounds

A flow controller design approach based on the /spl mu/-synthesis is proposed. Performances of the resulting controllers and the /spl Hscr//sup /spl infin// controllers designed based on the approach we proposed earlier (2000), are compared.

This paper presents a rational /spl Lscr//sub 1/ and mixed /spl Lscr//sub 1///spl Hscr//sub /spl infin// compensator design methodology for continuous time systems. The problem formulation involves finding a finite dimensional stabilizing feedback controller that minimizes the /spl Lscr/1 norm of a closed-loop transfer matrix subject to a frequency domain /spl Hscr//sub /spl infin// norm constraint on another closed-loop transfer matrix. It is shown that for a one-block problem the optimal solution can be approximated arbitrarily closely in terms of the closed-loop /spl Lscr//sub 1/ norm, by solving a sequence of convex optimization problems over linear matrix inequalities. Numerical example is provided to demonstrate the effectiveness of this approach.

Multiobjective frequency domain design aims to find a controller that gives desirable properties to several closed loop frequency responses simultaneously. This problem may be cast as a problem of finding a controller such that the worst-case /spl Hscr//sub /spl infin// norm, i.e. the largest among several /spl Hscr//sub /spl infin// norms, satisfies a prespecified bound. The authors define an upper bound, the /spl rho/ measure, for the worst-case /spl Hscr//sub /spl infin//, norm in terms of a scaled /spl Hscr//sub /spl infin// cost function. The authors show that the problem of finding a controller that minimizes /spl rho/ can be reduced to a finite dimensional convex program for the unknown scales and a standard /spl Hscr//sub /spl infin// problem. The authors give affine matrix inequalities for controller synthesis when the scales are restricted to constant matrices. A numerical example is used to illustrate the advantages of the authors' formulation, over the single objective /spl Hscr//sub /spl infin//, formulation, for solving multiobjective /spl Hscr//sub /spl infin// problems.

The theory of /spl mu/-synthesis introduced in [1, 2] provides, in principle, a broadly applicable theory for the optimal synthesis of multiloop feedback control laws that robustly meet performance and disturbance attenuation specifications despite unknown-but-bounded nonlinearities and parameter variations. Commercial MATLAB-based software packages implementing a crude approximation to the theory are available [3, 4], but these computer packages address the complex /spl mu/-synthesis problem via a somewhat flawed implementation of the original D-K iteration algorithm which involves the repetition of the following three operations on a suitable augmented closed-loop system transfer function: 1. Optimize a diagonal scaling frequency response matrix D(jw) for a fixed control law K(s). 2. Perform an ad hoc state space curve-fit to D(jw). 3. Use H/sup /spl infin// control to compute a control law K(s) with the diagonal scaling D(s) fixed. The curve-fitting of Step 2 has, until now, been a major obstacle to the realization of the original vision of a completely automated /spl mu/-synthesis procedure for robust control design. This paper describes new theoretical results and how they enable one to bypas the difficult and awkward curve-fitting of Step 2. The result is the first reliable computational algorithm for /spl mu/-synthesis controller design. The technique has been implemented on MATLAB. An example involving real /spl mu/-synthesis for the ACC Benchmark problem is included.

Design of gain-scheduled controllers has attracted wide attention in /spl Hscr//sub /spl infin// control. Within the framework of /spl lscr//sub 1/-optimal control, a novel method for gain-scheduled output-feedback control has been proposed recently using a special control structure. This paper extends this method to more general linear parameter-varying systems. Furthermore an explicit way of constructing the resulting gain-scheduled controllers is derived, and conditions for their existence are given. Finally, state-space formulas for these controllers are introduced. These formulas significantly facilitate an implementation and result in a relatively low complexity of the controller's parameter dependence.

This paper deals with the linear /spl Hscr//sub /spl infin// filtering problem for a class of regionally stable uncertain nonlinear systems subject to bounded disturbances and measurement noises. The nonlinear systems is represented by differential-algebraic equations where the system matrices are allowed to be rational functions of the state and uncertain parameters. For this class of systems, LMI conditions are proposed for ensuring a prescribed upper-bound on the /spl Lscr//sub 2/-gain of the input-to-estimation error operator for a given linear asymptotically stable filter. The result is based on polynomial Lyapunov functions. Then, using an appropriate parameterization of the Lyapunov function we extend the analysis result for designing linear filters in a /spl Hscr//sub /spl infin// sense via a convex optimization problem.

Attempts to solve the state-feedback H/sub 2//H/sub /spl infin// control problem by a LMI technique that allows for uncommon LMI solutions. In order to obtain a common controller ensuring the two performance criteria while allowing uncommon LMI solutions, we figure out what portion of the LMI solution should be constrained. Then, utilizing the freedom of the unconstrained portion, we propose an iterative method to obtain an updated controller gain which further improves the H/sub 2/ performance under the /spl Hscr//sub /spl infin// constraint. An illustrated example is included.

Deals with the direct design of state feedback mixed /spl Hscr//sub 2///spl Hscr//sub /spl infin//, control for sampled-data systems. In particular, a state feedback control design method is proposed to achieve the performance tradeoff between /spl Hscr//sub 2/ and /spl Hscr//sub /spl infin// objectives characterized by the Nash game approach in a continuous time domain.

The standard state space solutions to the /spl Hscr//sub /spl infin// control problem for linear time-invariant systems are generalized to nonlinear time-invariant systems. A class of local nonlinear (output feedback) /spl Hscr//sub /spl infin//-controllers are parameterized as nonlinear fractional transformations on contractive, stable nonlinear parameters. As in the linear case, the /spl Hscr//sub /spl infin// control problem is solved by its reduction to state feedback and output estimation problems, together with a separation argument. Sufficient conditions for /spl Hscr//sub /spl infin//-control problem to be locally solved are also derived with this machinery. >

In this paper, a behavioral version of the /spl Hscr//sub /spl infin// problem for continuous time, linear time invariant systems is formulated and solved. This general formulation, of which standard /spl Hscr//sub /spl infin// is a special case, provides added freedom in the design of optimal controllers, and can in fact be viewed as a means of designing optimal systems. In particular, the formulation presented allows for singular interconnections, which naturally occur when interconnecting systems. >

Chapter 9 - Cyberphysical Security Methods

6 - Design and Performance of Feedback Controllers

This paper deals with H/sub /spl infin////spl mu/ DIA control of the magnetic suspension system. H/sub /spl infin// DIA control is an H/sub /spl infin// control problem which treats a mixed Disturbance and an Initial-state uncertainty Attenuation (DIA) and supplies H/sub /spl infin// controls with good transients. H/sub /spl infin// DIA controller has a good initial response property, however its robust performance might be improved. We propose H/sub /spl infin////spl mu/ DIA Control which is to find a multi-objective controller to achieve both the H/sub /spl infin// DIA condition for good initial responses/transient responses and the structured singular value /spl mu/ condition for robust performance. We apply this proposed approach to the magnetic suspension system, and design a robust controller which has both good properties. Finally experimental results show effectiveness of the proposed control system design framework.

The dynamics of a web transport system are coupled and interactive among spans of web and rolls/rollers. As the process speed or variation of the speed is high, system friction and inertia of rotation of rolls could cause problems in implementation of observer techniques for tension estimation and control. In the author's previous study (see IEEE International Conference on Industrial Electronics, Control and Instrumentation, Denver, Colorado, USA (2001)), an observer-based tension feedback controller with friction and inertia compensation was proposed. However, the gains of observer and controller were determined based on the trial-and-error approach. This paper continues the author's previous study and presents an analytical approach for the gain design of observers in the time domain but design of controllers in the frequency domain. The linearization and decentralization techniques are implemented. Design of tension observers and feedback controllers with friction and inertia compensation is studied. Approaches for the gain design are discussed, and summarized procedures are given. The proposed analytical approach for design of tension observers and feedback controllers has been proven to be adequate by experiment.

A state feedback /spl Hscr//sub /spl infin//-suboptimal control problem on TSO(3) for a rigid spacecraft with three control torques and disturbances is addressed, the Hamilton-Jacobi inequality associated with a corresponding state feedback /spl Hscr//sub /spl infin//-suboptimal control problem on TS/sup 3/ is solved globally. The /spl Hscr//sub /spl infin//-suboptimal state feedback on TS/sup 3/ involves the Euler parameters and solves the original problem on TSO(3) when the initial values of the Euler parameters are appropriately chosen.