TOPICS IN STABILIZATION UNDER CONSTRAINTS AND SYNCHRONIZATION PROBLEMS

Xu Wang

All physical systems are operating under a variety of constraints. Control designs without taking these constraints into account will result in performance deterioration and even instability. A major part of the thesis is devoted to the constrained stabilization problems. The goal is to develop various controller design methodologies to achieve stabilization under different constraints. In the case where a linear system is subject to hard constrains on state and input, the notions of semi-global stabilization in the admissible set and recoverable region are explicitly related to certain structural properties of the systems. For a class of sandwich nonlinear systems consisting of cascaded linear systems and saturation elements, necessary and sufficient conditions for semi-global and global stabilization are presented. Under these conditions, a generalized low-gain design methodology is proposed to solve the stabilization problems. For linear system with input saturation and multiple time delays, upper bounds on the delays are found and corresponding controllers can be designed to achieve semi-global stabilization under input saturation and tolerable delays. When the issues related to internal stabilization are resolved, the research is directed to simultaneous stabilization problems. The focus here is linear system subject to input saturation. In the case where disturbances that are additive to the input, we complement the existing results in the literature by solving the simultaneous stabilization problems for discrete-time linear systems subject to input saturation. Then attention is paid to non-input-additive disturbances. This research is carried out using a progressive approach. The results are obtained and generalized from a simple double integrator to the most general linear systems. It is found that the simultaneous stabilization problems are solvable if the disturbances do not contained large frequency component corresponding to the open-loop eigenvalues on the stability margin. For those disturbances that meet this criterion, dynamical feedback controller can be constructed to achieve simultaneous stabilization. The rest of the thesis studies synchronization problems in multi-agent networks with uniform constant communication delays. Both homogeneous and heterogenous networks are considered. In the homogenous case, we assume that agents that are at most critically unstable. An achievable upper bound of delay tolerance is obtained which explicitly depends on agent dynamics and network topology. For any delay satisfying the proposed upper bounds, a controller design methodology without exact knowledge of the network topology is proposed so that the multi-agent synchronization in a set of networks can be achieved. For heterogeneous networks, under the assumption that the agents are introspective and right-invertible, synchronization problem can be solved for an arbitrarily given delay via decentralized dynamical controllers. The synchronization with output regulation problem in a heterogeneous network is also investigated and solved under mild conditions. The proposed design method can be applied to the output formation problem.

TOPICS IN STABILIZATION UNDER CONSTRAINTS AND SYNCHRONIZATION PROBLEMS

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