严格反馈Markov 跳跃非线性系统风险灵敏度设计

在无限时区风险灵敏度指标下,研究了一类具有严格反馈形式的 Markov 跳跃非线性系统的控制器设计问题.首先,将此问题的可解性转化为一类 HJB 方程的可解性;然后根据此方程,构造性地给出一个与模态无关的控制器,此控制器可保证闭环系统是依概率有界的,且风险灵敏度指标不大于任意给定的正常数,特别地,当噪声项在原点处消逝时,能够确保风险灵敏度指标为零;最后,通过仿真例子验证了理论结果的正确性.

Risk-sensitive control design for strict-feedback nonlinear stochasticsystems with Markovian jump

The controller design for a class of strict-feedback nonlinear stochastic systems with Markovian jump under a
risk-sensitive cost function criterion is studied. Firstly, this problem is solvable if a class of HJB equation is solvable. Then,
a constructive control law, which is independent of the regime, is designed based on this HJB equation, which guarantees any
desired positive level of long-term average cost for a given risk-sensitivity parameter and achieve boundedness in probability
for the closed-loop system. As a special case, when the vector fields for the disturbance vanish at the origin, the control law
can actually guarantee a zero long-term average cost for the closed-loop system. Finally, an example is given to illustrate the
correctness of the main results.