Robust hybrid predictive control of nonlinear systems
The paper considers nonlinear systems with uncertain variables and input constraints, described by \[ \dot x=f(x)+G(x)u+W(x)\theta(t), \quad x\in\mathbb R^n, \quad u\in\mathbf U\subset\mathbb R^m,\quad \theta(t)\in\Theta\subset\mathbb R^k, \tag{1} \] where \(x\) is the vector of state variables, \(u\) is the vector of constrained manipulated inputs, \(\theta(t)\) is the vector of uncertain bounded variables and \(f(0)=0\). The vector function \(f(x)\) and the matrices \(G(x)\) and \(W(x)\) are assumed to be sufficiently smooth. For the system (1), the paper presents a robust hybrid predictive control structure that provides a safety net for the implementation of any model predictive control (MPC) formulation, designed with or without taking uncertainty into account. The approach uses a Lyapunov-based bounded robust controller, for which an explicit characterization of the region of robust closed-loop stability can be obtained. Thus, a stability region within which any available MPC formulation can be implemented is provided. This is achieved by devising a set of switching laws that orchestrate switching between MPC and the bounded robust controller in a way that exploits the performance of MPC whenever possible, while using the bounded controller as a fall-back controller that can be switched in at any time to maintain robust closed-loop stability in the event the predictive controller fails to yield a control move or leads to instability. As an example, the implementation of the robust hybrid predictive control structure is demonstrated by simulations of a chemical process.
scientific article; zbMATH DE number 2137842
scientific article