This paper uses the commutant lifting theorem for representations of the nest algebra to deal with the optimal control of infinite dimensional linear time-varying systems. We solve the model matching problem and a certain optimal feedback control problem, each of which corresponds with one type of four-block problem. We also obtain a new formula for the optimal performance and prove the existence of an optimal controller.
This paper presents a finite-time stabilization method for the integrator chain via optimal control techniques by introducing a tailored cost function. We analyze key properties of the resulting value function to derive the corresponding Hamilton-Jacobi-Bellman equation. Numerical simulations illustrate the effectivene...
In non-autonomous time-optimal control problems the question of the sufficiency of the maximum principle is considered. We also briefly discuss the question of uniqueness of optimal control. New conditions are obtained that guarantee the sufficiency of the maximum principle in terms of convex analysis, properties of ma...
It is shown that there exists a piecewise constant feedback controller such that the system can achieve the approximate stabilization property under arbitrary switching signal.
In this work we are concerned with the controllability of time-varying lumped control systems governed by a semilinear differential equation. We consider the semilinear system as a perturbation of a linear system. Assuming the underlying linear system is controllable, and the nonlinear forcing function satisfies a boun...
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