Locally optimal controllers and globally inverse optimal controllers

In this paper we consider the problem of global asymptotic stabilization with prescribed local behavior. We show that this problem can be formulated in terms of control Lyapunov functions. Moreover, we show that if the local control law has been synthesized employing a LQ approach, then the associated Lyapunov function can be seen as the value function of an optimal problem with some specific local properties. We illustrate these results on two specific classes of systems: backstepping and feedforward systems. Finally, we show how this framework can be employed when considering the orbital transfer problem

New advances in H∞ control and filtering for nonlinear systems

The main objective of this special issue is to summarise recent advances in H∞ control and filtering for nonlinear systems, including time-delay, hybrid and stochastic systems. The published papers provide new ideas and approaches, clearly indicating the advances made in problem statements, methodologies or applications with respect to the existing results. The special issue also includes papers focusing on advanced and non-traditional methods and presenting considerable novelties in theoretical background or experimental setup. Some papers present applications to newly emerging fields, such as network-based control and estimation

Power system damping controllers design using a backstepping control technique

The objective of this dissertation is to design and coordinate controllers that will enhance transient stability of power systems subject to large disturbances. Two specific classes of controllers have been investigated, the first one is a type of supplementary signals added to the excitation systems of the generating units, and the second is a type of damping signal added to a device called a Static Var Compensator that can be placed at any node in the system. To address a wide range of operating conditions, a nonlinear control design technique, called backstepping control, is used. While these two types of controllers improve the dynamic performance significantly, a coordination of these controllers is even more promising. Control coordination is presented in two parts. First part concerns simultaneous optimization of selected control gains of exciter and SVC in coping with the complex nature of power systems. Second part proposes a combination of reinforcement learning and a backstepping control technique for excitation control system. The reinforcement learning progressively learns and adapts the backstepping control gains to handle a wide range of operating conditions. Results show that the proposed control technique provides better damping than conventional power system stabilizers and backstepping fixed gain controllers

3 sampled-data control of nonlinear systems

This chapter provides some of the main ideas resulting from recent developments in sampled-data control of nonlinear systems. We have tried to bring the basic parts of the new developments within the comfortable grasp of graduate students. Instead of presenting the more general results that are available in the literature, we opted to present their less general versions that are easier to understand and whose proofs are easier to follow. We note that some of the proofs we present have not appeared in the literature in this simplified form. Hence, we believe that this chapter will serve as an important reference for students and researchers that are willing to learn about this area of research