Guaranteed robustness properties of multivariable, nonlinear, stochastic optimal regulators

By John N. Tsitsiklis, M. Athans. 1983

We study the robustness of optimal regulators for non-linear, deterministic and stochastic, multi-input dynamical systems, under the assumption that all state variables can be measured. We show that, under mild assumptions, such nonlinear regulators have a guaranteed infinite gain margin; moreover, they have a guaranteed 50 percent gain reduction margin and a 60 degree phase margin, in each feedback channel, provided that the system is linear in the control and the penalty to the control is quadratic, thus extending the well-known properties of LQ regulators to nonlinear optimal designs. These results are also valid for infinite horizon, average cost, stochastic optimal control problems.

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1. Wenwu Yu
2. Guanrong Chen
3. Yongcan Cao
4. Wei Ren
5. Guanghui Wen
6. Zhongkui Li
7. Housheng Su
8. Z. Duan

Citations in the corpus

• An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination (2012, background): “In the control systems society, some pioneering works are generally referred to [5], [6], where an asynchronous agreement problem was studied for distributed decision-making problems.”
• Constructive nonlinear control: a historical perspective (2001, methodology): “An analysis of stability margins for nonlinear optimal regulators was given by Glad (1984), and Tsitsiklis and Athans (1984).”
• Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems (2001, background): “This robustness is equivalent to that of optimal regulators [6], [ 22 ] and follows from the connection between optimality and passivity.”