Robust constrained model predictive control using linear matrix inequalities
Automatica (Journal of IFAC)
Robust Solutions to Uncertain Semidefinite Programs
SIAM Journal on Optimization
Semidefinite Programming Relaxation for NonconvexQuadratic Programs
Journal of Global Optimization
On the gap between the quadratic integer programming problem and its semidefinite relaxation
Mathematical Programming: Series A and B
Survey Constrained model predictive control: Stability and optimality
Automatica (Journal of IFAC)
Optimization over state feedback policies for robust control with constraints
Automatica (Journal of IFAC)
| Hi-index | 22.14 |
In this paper, we investigate the problem of nonlinearity (and non-convexity) typically associated with linear state-feedback parameterizations in the Robust Model Predictive Control (RMPC) for uncertain systems. In particular, we propose two tractable approaches to compute an RMPC controller-consisting of both a causal, state-feedback gain and a control-perturbation component-for linear, discrete-time systems involving bounded disturbances and norm-bounded structured model-uncertainties along with hard constraints on the input and state. Both the state-feedback gain and the control-perturbation are explicitly considered as decision variables in the online optimization while avoiding nonlinearity and non-convexity in the formulation. The proposed RMPC controller-computed through LMI optimizations-is responsible for steering the uncertain system state to a terminal invariant set. Numerical examples from the literature demonstrate the advantages of the proposed scheme.