Reachset Model Predictive Control for Disturbed Nonlinear Systems

Robust Output Feedback MPC for Linear Systems via Interpolation Technique

This paper considers stabilization of discrete-time linear systems, where network exists for transmitting the sensor and controller information, and arbitrary bounded packet loss occurs between the sensor and controller, and between the controller and actuator. The stabilization of this system is transformed into the robust stabilization of a set of systems. A novel stability result is given for this system, which is specially applied on model predictive control (MPC) that explicitly considers the satisfaction of input and state constraints. A synthesis approach of MPC, parameterizing the infinite horizon control moves into a single state feedback law, is proposed. A simulation example is given to illustrate the effectiveness of the proposed MPC.

Explicit Model Predictive Control (MPC) is an attractive control strategy, especially when one aims at a fast, computationally less demanding implementation of MPC. Although leading to a fast implementation of optimization-based control, the main downside of explicit MPC is its high complexity in terms of memory occupancy, which often limits practical applicability of such a control methodology. Therefore in this paper we propose to obtain simple explicit MPC controllers that provide guarantees of recursive satisfaction of input and state constraints. The task is accomplished by optimizing, off-line, the parameters of the feedback law such that an integrated square error between the optimal, but complex controller and its simpler replacement is minimized. We show that the task can be formulated as a quadratic optimization problem which always yields an admissible solution. In this way, suboptimality of simple feedbacks with respect to their complex optimal counterparts is significantly mitigated.

This work investigates the event‐driven model predictive control problem for perturbed nonlinear systems with input and state constraints. Firstly, a new event‐driven triggering condition, considering the gradient and accumulation of the error between the optimal and actual states at adjacent moments with a state‐dependent relative threshold is designed with a guaranteed positive inter‐event time to avoid Zeno behaviour. Secondly, an error gradient and accumulation type event‐driven model predictive control framework is designed based on the new triggering condition and the dual‐mode strategy, for effectively reducing the calculation and communication burden of the model predictive control controller while ensuring desired control performance. Furthermore, the feasibility and the input‐to‐state practical stability (ISpS) of gradient and accumulation‐type event‐driven model predictive control are rigorously guaranteed theoretically. At last, the simulation results are provided to validate the this algorithm.

We present a rigorous framework for the study of distributed spatially invariant systems with input and state constraints. The proposed approach is based on blending tools from operator theory and Fourier analysis of spatially invariant systems with receding horizon control and multi parametric quadratic programming (MPQP). Our contributions are twofold: on one hand, we extend the recent results of Bamieh et al. on infinite-horizon optimal control of spatially invariant systems to finite receding horizon control with input and state constraints. On the other hand, our results can be interpreted as an extension of the finite dimensional MPQP-based analysis of receding horizon control to distributed, spatially invariant systems. It is assumed that the dynamics of each subsystem is uncoupled to the others, but the coupling appears through the finite horizon cost function. Specifically, we prove that for spatially invariant systems with constraints, optimal receding horizon controllers are piecewise affine (represented as a convolution sum plus an offset). Moreover, the kernel of each convolution sum decays exponentially in the spatial domain mirroring the unconstrained infinite-horizon case. Simulation results are provided for a simple example with 5 identical systems coupled in a loop.

Discussion on: “Improved MPC Design based on Saturating Control Laws”

In this article, we propose a novel economic model-predictive control (MPC) algorithm for a group of disturbed linear systems and implement it in a distributed manner. The system consists of multiple subsystems interacting with each other via dynamics and aims to optimize an economic objective. Each subsystem is subject to constraints both on states and inputs as well as unknown but bounded disturbances. First, we divide the computation of control inputs into several local optimization problems based on each subsystem's local information. This is done by introducing compatibility constraints to confine the difference between the actual information and the previously published reference information of each subsystem, which is the key feature of the proposed distributed algorithm. Then, to ensure the satisfaction of both state and input constraints under disturbances, constraints are tightened on the state and the input of nominal systems by considering explicitly the effect of uncertainties. Moreover, based on an overall optimal steady state, a dissipativity constraint and a terminal constraint are designed and incorporated in the local optimization problems to establish recursive feasibility and guarantee stability for the resulting closed-loop system. Finally, the efficiency of the distributed economic MPC algorithm is demonstrated in a building temperature control case study.

High-precision positioning of two underwater mobile robots is investigated in this work. To achieve good performance in underwater communication, control algorithms are implemented to maintain the position of the receiver robot aligned with that of the transmitter in the presence of measurement noise and process uncertainty. Although recent research works have successfully integrated control algorithms with Extended Kalman Filter (EKF) estimator to track the desired position of the transmitter, other aspects besides the convergence to the equilibrium point such as operational constraints and input constraints were not taken into account within these controllers. Such inability of these control algorithms may degrade the performance of the controlled process. Motivated by the above considerations, a tracking Model Predictive Control (MPC) with an EKF-based estimator is developed to both estimate the process states online and drive the actual system to the desired equilibrium point while meeting input and state constraints. The closed-loop stability and the recursive feasibility of the proposed tracking MPC scheme are rigorously proved. To demonstrate the applicability of the proposed control design, the performance of the tracking MPC with that of the conventional Proportional (P), Proportional Integral Derivative (PID), and Linear Quadratic Regulator (LQR) controllers are compared.

Optimal control of grinding mill circuit using model predictive static programming: A new nonlinear MPC paradigm

A critical engineering challenge in quantum technology is the accurate control of quantum dynamics. Model-based methods for optimal control have been shown to be highly effective when theory and experiment closely match. Consequently, realizing high-fidelity quantum processes with model-based control requires careful device characterization. In quantum processors based on cold atoms, the Hamiltonian can be well-characterized. For superconducting qubits operating at milli-Kelvin temperatures, the Hamiltonian is not as well-characterized. Unaccounted for physics (i.e., mode discrepancy), coherent disturbances, and increased noise compromise traditional model-based control. This work introduces model predictive control (MPC) for quantum control applications. MPC is a closed-loop optimization framework that (i) inherits a natural degree of disturbance rejection by incorporating measurement feedback, (ii) utilizes finite-horizon model-based optimizations to control complex multi-input, multi-output dynamical systems under state and input constraints, and (iii) is flexible enough to develop synergistically alongside other modern control strategies. We show how MPC can be used to generate practical optimized control sequences in representative examples of quantum state preparation. Specifically, we demonstrate for a qubit, a weakly-anharmonic qubit, and a system undergoing crosstalk, that MPC can realize successful model-based control even when the model is inadequate. These examples showcase why MPC is an important addition to the quantum engineering control suite.

We present an analytical and computational framework using the theory of Koopman operator to design dual-mode model predictive control (MPC) for nonlinear control systems. Dual-mode MPC incorporates stability and performance constraints in the controller and remains a challenging problem to solve for systems involving nonlinear dynamics. We exploit the spectral properties of the Koopman operator to provide a systematic approach for the design of optimal control, guaranteeing the stability of the feedback control system. The optimal cost function is also used for characterizing the maximal invariant set, which serves as the terminal set in the design of finite-horizon MPC. The finite horizon MPC relies on lifting nonlinear system dynamics using Koopman eigenfunctions to provide a linear approach for the design of MPC with state and input constraints.

This paper studies the model predictive control (MPC) of the networked control systems (NCSs) where arbitrary bounded deterministic network-induced delays and packet losses may occur in both sensor to controller and controller to actuator links. A new augmented model, which is specially suitable to the on-line refreshed control law, is proposed, based on which an approach of networked MPC is proposed by extending the previous one for NCS with only packet losses. It is shown that closed-loop stability is guaranteed by the proposed approach, satisfying the input and state constraints. A numerical example is given to illustrate the effectiveness of the proposed MPC.

Model predictive control (MPC) is an efficient and growing approach to power converter control. This paper proposes an improved and simplified model predictive current control (MPCC) technique for a four-level nested neutral point clamped (4L-NNPC) converter. Conventional MPCC exhibits better performances as compared to the conventional linear control system such as fast dynamic response, consideration of the system constraints, and nonlinearities. However, the application of the conventional model predictive current control (MPCC) approach on complex systems provokes a significant number of calculations, which is the main hurdle to its practical implementation. To fix this flaw, this paper proposes an effective algorithm to shorten the execution time of the conventional MPCC. In this proposed technique, 216 current predictions of the conventional MPCC are skipped and converted into one required voltage vector (RVV) prediction. With this equivalent reference voltage transformation, the calculation burden of MPCC is significantly reduced, while the output performance is not influenced. The results of the simplified MPCC for the 4L-NNPC converter are analyzed and compared with the conventional MPCC. The computational time is reduced by 19.56% using the simplified MPCC, while keeping an approximately similar error of output currents. The switching frequency and total harmonic distortion (THD) of the proposed method are reduced by 8.16% and 0.07%, respectively, as compared to the conventional technique. These results demonstrate the fact that that the performance of a conventional MPCC is enhanced with the proposed MPCC. The proposed algorithm can be applied to several inverter topologies.

Effective recursive parallelotopic bounding for robust output-feedback control

Model Predictive Control (MPC) has the advantage of including constraints into the optimization. By combining MPC with Feedback Linearization (FBL) it is possible to use linear, discrete time MPC algorithms with nonlinear models. This way the constraints on the control systems, thrusters and aerodynamic surface deflections, and on the attitude of the vehicle can be integrated into the controller synthesis. The main disadvantage of this type of controller is the lack of robustness when uncertainties enter the system. This paper therefore improves the nominal FBL-MPC controller by replacing the Quadratic Programming algorithm with a minmax MPC technique involving Linear Matrix Inequalities. Uncertainties on the nonlinear aerodynamic coecients are used as a source of disturbances. By mapping these uncertainties to a linear state space model as used by the MPC controller, a polytopic set of uncertainty models is created that can be used by the min-max algorithm to minimize the performance cost over the worst case model from the uncertainty set. This approach will be illustrated using a model of the X-38 re-entry vehicle flying along a predefined trajectory with active input and state constraints. The results show that the robustness is improved significantly when compared to the nominal controller with the same uncertainties.