Vijaya-Sekhar Chellaboina

TL;DR: In this paper, the authors generalize Poincare's method to dynamical systems possessing left-continuous flows to address the stability of limit cycles and periodic orbits of leftcontinuous, hybrid, and impulsive systems.

TL;DR: It is shown that the control Lyapunov function guaranteeing closed-loop stability is a solution to the steady-state Bellman equation for the controlled system and thus guarantees both optimality and stability.

Abstract: One of the fundamental problems in feedback control design is the ability of the control system to reject uncertain exogenous disturbances. Since a single performance objective is seldom adequate to capture multiple and often conflicting system disturbances, in this paper we develop a Riccati equation approach for mixed H2/L1 controller synthesis via fixed-order dynamic compensation. This multiobjec2 tive problem is treated by forming a convex combination of both the H2 (quadratic) and L1 bound (worst-case peak amplitude response) performance measures. For flexibility in controller synthesis, we adopt the approach of fixed-structure controller design which allows consideration of arbitrary controller structures, including order, internal structure, and decentralization. Finally, using a quasi-Newton continuation algorithm, we demonstrate the effectiveness of the proposed mixed-norm H2/L1 Riccati equation approach via several design examples.

TL;DR: In this article, the authors develop a unied framework to address the problem of optimal nonlinear robust control for linear uncertain systems, and transform a given robust control problem into an optimal control problem by properly modifying the cost functional to account for the system uncertainty.

TL;DR: In this paper, a unified framework for discrete-time optimal nonlinear analysis and feedback control is developed to guarantee the stability and optimality of closed-loop nonlinear systems by means of a Lyapunov function, which can clearly be seen as the solution to the steady-state form of the discrete time Bellman equation.