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A robust, adaptive Model Predictive Control (MPC) approach for asymptotically stable, constrained linear time-varying (LTV) systems with multiple inputs and outputs is proposed. The approach consists of two-steps, carried out on-line with a receding horizon strategy. In the first one, a real-time Set Membership identification algorithm exploits the measured input–output data and the available prior knowledge to build and refine a set of admissible models of the plant (Feasible Parameter Set, FPS). This set is guaranteed to contain also the true system dynamics under the considered working assumptions. In the second step, a robust finite-horizon optimal control problem is formulated and solved. The variation of system dynamics is taken into account by inflating the FPS over the prediction horizon, according to worst-case bounds, assumed a priori, on the parameters' rate of change. The resulting optimal control sequence guarantees that the outputs of all possible plants inside the FPS satisfy the operational constraints, also considering all possible future parameter changes. The main theoretical properties of the proposed approach are demonstrated and the method is showcased in numerical simulations, highlighting the fundamental improvement over previous approaches not designed for LTV systems. [ABSTRACT FROM AUTHOR]

A data-driven method to design reference tracking controllers for nonlinear systems is presented. The technique does not derive explicitly a model of the system, rather it delivers directly a time-varying state-feedback controller by combining an on-line and an off-line scheme. Like in other on-line algorithms, the measurements collected in closed-loop operation are exploited to modify the controller in order to improve the tracking performance over time. At the same time, a predictable closed-loop behavior is guaranteed by making use of a batch of available data, which is a feature of off-line algorithms. The feedback controller is parameterized with kernel functions and the design approach exploits results in set membership identification and learning by projections. Under the assumptions of Lipschitz continuity and stabilizability of the system’s dynamics, it is shown that if the initial batch of data is informative enough, then the resulting closed-loop system is guaranteed to be finite gain stable. In addition to the main theoretical properties of the approach, the design algorithm is demonstrated experimentally on a water tank system. [ABSTRACT FROM AUTHOR]

The problem of experiment design for constrained linear systems with multiple inputs is addressed. A parametric model of the system is considered. The presented theoretical results provide a guideline on how to design experiments that minimize the worst-case identification error, as measured by the radius of information of the set of feasible model parameters, calculated in any norm. In addition, it is shown that an alternative, simpler approach can be employed when input constraints are symmetric and the worst-case identification error is minimized in either 1 - or ∞ -norm. For such cases, on the basis of the derived results, a computationally tractable algorithm for the experiment design is proposed. The presented results are valid for a general model representation, which admits the commonly used finite impulse response model as a special case. The features of the presented method are illustrated in a numerical example. [ABSTRACT FROM AUTHOR]

An adaptive control algorithm for open-loop stable, constrained, linear, multiple input multiple output systems is presented. The proposed approach can deal with both input and output constraints, as well as measurement noise and output disturbances. The adaptive controller consists of an iterative set membership identification algorithm, that provides a set of candidate plant models at each time step, and a model predictive controller, that enforces input and output constraints for all the plants inside the model set. The algorithm relies only on the solution of standard convex optimization problems that are guaranteed to be recursively feasible. The experimental results obtained by applying the proposed controller to a quad-tank testbed are presented. [ABSTRACT FROM AUTHOR]