Equivalence in Predictive Control Formulations. In this chapter, the first equivalence of model predictive controller (MPC) is constructed based on Diophantine equations leading to a closed-form solution in the unconstrained case. The second equivalence is given towards the family of state-space based MPC controllers which is used to derive an explicit solution for the constrained case.
Dutta, A. Design and certification of industrial predictive controllers. Ghent University, 2014.
Certified Predictive Control without Terminal Conditions. This chapter is devoted to feasibility, stability analysis of input-output MPC without imposing artificial terminal conditions and where fewer changes are made to future controls than the horizon over which the process dynamics are predicted. Constraint satisfaction (i.e. feasibility) can be guaranteed for all time and for all disturbances if the initial state is inside a set which is invariant i.e. future state evolutions remain within this set. Infinite time feasibility thus ensures that trajectories remain bounded always, directly leading to the notion of practical stability.
Abhishek Dutta, et al. Certification of a class of industrial predictive controllers without terminal conditions. 53rd IEEE Conference on Decision and Control, 2014.
Abhishek Dutta, et al. Robust penalty adaptive model predictive control (PAMPC) of constrained, underdamped, noncollocated systems. Journal of Vibration and Control 22.2: 549-558, 2016.
Penalty Adaptive Predictive Control. In this chapter, penalty adaptation is used as a mechanism to deliver a more rigorous asymptotic stability derivation of the nominal closed loop MPC without terminal conditions. This is achieved by adjusting the weights of the future control moves in a way that makes the constraints inactive. Hence closed form polynomial expression for the adapted linear MPC can be derived which allows to specify the corresponding stability margins.
Switched Nonlinear Predictive Control. This chapter derives a formal proof of convergence of nonlinear MPC to locally optimal solution and a tuning prescription to guarantee this property. The developments on persistent and recursive feasibility, stability without terminal conditions have been extended to piecewise affine systems. The presented NMPC techniques that are fast, simple and do not use terminal conditions, are demonstrated over automatic transmission control and are readily adoptable by the industry.
Abhishek Dutta, et al. Comparison of two-level NMPC and ILC strategies for wet-clutch control. Control Engineering Practice 22: 114-124, 2014.
Distributed Nonlinear Predictive Control. In this chapter, NMPC controllers without terminal conditions are used in a distributed setup where each one optimizes a global cost with respect to itself and communicates once to its adjacent neighbor. A formal proof is developed to show that such a policy leads to guaranteed improvement in the global cost. A hydrostatic drivetrain is used as a benchmark to show that the proposed distributed NMPC approach is applicable for fast, interacting, nonlinear, constrained industrial systems.
Dutta, Abhishek, Clara Ionescu, and Robain De Keyser. A pragmatic approach to distributed nonlinear model predictive control: Application to a hydrostatic drivetrain. Optimal Control Applications and Methods 36.3: 369-380, 2015.
