Uncertainty-averaging approach to output feedback optimal guaranteed cost control of uncertain systems. (English) Zbl 0853.93065

Savkin, A. V.; Petersen, I. R.

J. Optimization Theory Appl. 88, No. 2, 321-337 (1996).

The authors are well known experts on control theory of systems with uncertainties. In the article under review they introduce a new class of systems with a structural uncertainty. The systems are linear, modelled by the equations: \[ \begin{aligned} \dot x(t) & = A(t) x(t) + B(t) u(t) + C_s (t) \xi (t), \\ \dot y(t) & = H(t) x(t) + \sum^k_{s = 1} V_s \xi_s (t), \\ \dot z_i (t) & = K_i (t) x(t) + G_i (t) u(t),\;i = 1, 2, \dots, k, \end{aligned} \] where \(x \in \mathbb{R}^n\) is the state, \(u \in \mathbb{R}^m\) is the control, \(y \in \mathbb{R}^t\) is the observation, \(\xi\) is the uncertainty input vector, \(z\) the uncertainty output, while all capital letters denote appropriate matrices, whose entries are functions bounded and piecewise continuous on \([0,T]\). The relation between the uncertainty input and control is given in vector form: \(\xi (t) = \Phi (t,x (.) |^t_0\), \({\mathbf u} (.) |^t_0)\).
Structural uncertainties are introduced, obeying an averaged integral quadratic constraint. This system is reduced to a pair of parametrized Riccati equations. The authors construct a controller, and prove that this controller satisfies the required bounds, and is a guaranteed cost controller. The authors follow the general ideas of the \(S\)-procedure discussed by A. M. Megretsky and S. Treil in [J. Math. Syst. Estim. Control 3, 301-319 (1993; Zbl 0781.93079)], but with differential initial conditions. They show that their system is more general, and that the results of Megretsky and Treil may be easily obtained after a minor modification of their system.

Reviewer: V.Komkov (Roswell)

MSC:

93C41	Control/observation systems with incomplete information
49N10	Linear-quadratic optimal control problems
93B52	Feedback control

Keywords:

\(S\)-procedure; structural uncertainty; integral quadratic constraint; guaranteed cost

Citations:

Zbl 0781.93079

References:

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