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This article considers the $mathcal{H}_infty$ static output-feedback control for linear time-invariant uncertain systems with polynomial dependence on probabilistic time-invariant parametric uncertainties. By applying polynomial chaos theory, the control synthesis problem is solved using a high-dimensional expanded system which characterizes stochastic state uncertainty propagation. A closed-loop polynomial chaos transformation is proposed to derive the closed-loop expanded system. The approach explicitly accounts for the closed-loop dynamics and preserves the $mathcal{L}_2$-induced gain, which results in smaller transformation errors compared to existing polynomial chaos transformations. The effect of using finite-degree polynomial chaos expansions is first captured by a norm-bounded linear differential inclusion, and then addressed by formulating a robust polynomial chaos based control synthesis problem. This proposed approach avoids the use of high-degree polynomial chaos expansions to alleviate the destabilizing effect of truncation errors, which significantly reduces computational complexity. In addition, some analysis is given for the condition under which the robustly stabilized expanded system implies the robust stability of the original system. A numerical example illustrates the effectiveness of the proposed approach.
Symbolic control is a an abstraction-based controller synthesis approach that provides, algorithmically, certifiable-by-construction controllers for cyber-physical systems. Current methodologies of symbolic control usually assume that full-state info
A probabilistic performance-oriented controller design approach based on polynomial chaos expansion and optimization is proposed for flight dynamic systems. Unlike robust control techniques where uncertainties are conservatively handled, the proposed
This paper addresses the mean-square optimal control problem for a class of discrete-time linear systems with a quasi-colored control-dependent multiplicative noise via output feedback. The noise under study is novel and shown to have advantage on mo
This paper investigates the cooperative control of multiple unmanned and manned vehicles via an output containment control approach for heterogeneous discrete-time multiagent systems. The unmanned vehicles act as leading vehicles to guide the manned
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