Abstract
A simplified model predictive control algorithm is designed for discrete-time Markov jump systems with mixed uncertainties. The mixed uncertainties include model polytope uncertainty and partly unknown transition probability. The simplified algorithm involves finite steps. Firstly, in the previous steps, a simplified mode-dependent predictive controller is presented to drive the state to the neighbor area around the origin. Then the trajectory of states is driven as expected to the origin by the final-step mode-independent predictive controller. The computational burden is dramatically cut down and thus it costs less time but has the acceptable dynamic performance. Furthermore, the polyhedron invariant set is utilized to enlarge the initial feasible area. The numerical example is provided to illustrate the efficiency of the developed results.
Highlights
Hybrid systems are a class of dynamical systems denoted by an interaction between the continuous and discrete dynamics
The notations are as follows: Rn denotes a ndimensional Euclidean space, AT stands for the transpose of a matrix, E{⋅} denotes the expectation of the stochastic process or vector, a positive-definite matrix is described as P > 0, I means the unit matrix with appropriate dimension, and ∗ means the symmetric term in a symmetric matrix
The discrete-time Markov stochastic process {rk, k ≥ 0} takes values in a finite set Γ, where Γ contains σ modes of system
Summary
Hybrid systems are a class of dynamical systems denoted by an interaction between the continuous and discrete dynamics. MJS presents a stochastic Markov chain to describe the random changes of system parameters or structures, where the dynamic of MJS is switching among the models governed by a finite Markov chain. Due to this superiority, MJS has been widely investigated during the last twenty years. The final step of robust mode-independent MPC is devised to force the state towards the origin regardless of model uncertainty and transition probability uncertainty This simplified MPC dramatically reduces the burden of computation with minor performance loss, which implies good balance between the calculation time and dynamical performance. The notations are as follows: Rn denotes a ndimensional Euclidean space, AT stands for the transpose of a matrix, E{⋅} denotes the expectation of the stochastic process or vector, a positive-definite matrix is described as P > 0, I means the unit matrix with appropriate dimension, and ∗ means the symmetric term in a symmetric matrix
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