In this brief, we consider the constrained optimization problem underpinning model predictive control (MPC). We show that this problem can be decomposed into an unconstrained optimization problem with the same cost function as the original problem and a constrained optimization problem with a modified cost function and dynamics that have been precompensated according to the solution of the unconstrained problem. In the case of linear systems subject to a quadratic cost, the unconstrained problem has the familiar LQR solution and the constrained problem reduces to a minimum-norm projection. This implies that solving linear MPC problems is equivalent to precompensating a system using LQR and applying MPC to penalize only the control input. We propose to call this a constraint-separation principle and discuss the utility of both constraint separation and general decomposition in the design of MPC schemes and the development of numerical solvers for MPC problems.
For linear time-invariant systems, a separation principle holds: stable observer and stable state feedback can be designed for the time-invariant system, and the combined observer and feedback will be stable. For non-linear systems, a local separation principle holds around steady-states, as the linearized system is time-invariant. This paper addresses the issue of a non-linear separation principle on Lie groups. For invariant systems on Lie groups, we prove there exists a large set of (time-varying) trajectories around which the linearized observer-controler system is time-invariant, as soon …
The cooperative output regulation problem of linear multi-agent systems was formulated and studied by the distributed observer approach in [20, 21]. Since then, several variants and extensions have been proposed, and the technique of the distributed observer has also been applied to such problems as formation, rendezvous, flocking, etc. In this chapter, we will first present a more general formulation of the cooperative output regulation problem for linear multi-agent systems that includes some existing versions of the cooperative output regulation problem as special cases. Then, we will descr…
This paper proposes a novel hierarchical model predictive control (MPC) strategy that guarantees overall system stability. This method differs significantly from previous approaches to guaranteeing overall stability, which have relied upon a multi-rate framework where the inner loop (low level) is updated at a faster rate than the outer loop (high level), and the inner loop must reach a steady-state within each outer loop time step. In contrast, the method proposed in this paper is aimed at stabilizing the origin of an error system characterized by the difference between the inner loop state a…
The communication channels used to convey information between the components of wireless networked control systems (WNCSs) are subject to packet losses due to time-varying fading and interference. We consider a wireless networked control scenario, where the packet loss occurs in both the sensor-controller link (sensing link) and the controller-actuator link (actuation link). Moreover, we consider one time-step delay mode observations of the actuation link. While the problems of state feedback optimal control and stabilizability conditions for systems with one time-step delay mode observations …
The core arguments used in various proofs of the extremal principle and its extensions as well as in primal and dual characterizations of approximate stationarity and transversality of collections of sets are exposed, analyzed and refined, leading to a unifying theory, encompassing all existing approaches to obtaining 'extremal' statements. For that, we examine and clarify quantitative relationships between the parameters involved in the respective definitions and statements. Some new characterizations of extremality properties are obtained.
A Nonlinear Separation Principle via Contraction Theory: Applications to Neural Networks, Control, and Learning
Center for Control, Dynamical Systems, and Computation, UC Santa Barbara（控制、动态系统与计算中心，加州大学圣巴巴拉分校）；Department of Electronics and Telecommunications, Politecnico di Torino（电子与电信系，托里诺理工学院）；Graduate School of Advanced Science and Engineering, Hiroshima University（先进科学与工程研究生院，广岛大学）
In this article, we introduce decentralized Kalman filters for linear quadratic deep structured teams. The agents in deep structured teams are coupled in dynamics, costs and measurements through a set of linear regressions of the states and actions (also called deep states and deep actions). The information structure is decentralized, where every agent observes a noisy measurement of its local state and the global deep state. Since the number of agents is often very large in deep structured teams, any naive approach to finding an optimal Kalman filter suffers from the curse of dimensionality. …
It is well known that quantum continuous observations and nonlinear filtering can be developed within the framework of the quantum stochastic calculus of Hudson-Parthasarathy. The addition of real-time feedback control has been discussed by many authors, but the foundations of the theory still appear to be relatively undeveloped. Here we introduce the notion of a controlled quantum flow, where feedback is taken into account by allowing the coefficients of the quantum stochastic differential equation to be adapted processes in the observation algebra. We then prove a separation theorem for quan…
Norwegian University of Science and Technology（挪威科技大学）；BASF SE（巴斯夫公司）；Imperial College London（帝国理工学院）
Nonlinear model predictive control (NMPC) is an efficient approach for the control of nonlinear multivariable dynamic systems with constraints, which however requires an accurate plant model. Plant models can often be determined from first principles, parts of the model are however difficult to derive using physical laws alone. In this paper a hybrid Gaussian process (GP) first principles modeling scheme is proposed to overcome this issue, which exploits GPs to model the parts of the dynamic system that are difficult to describe using first principles. GPs not only give accurate predictions, b…
This work presents a suboptimality study of a particular model predictive control with a stage cost shaping based on the ideas of reinforcement learning. The focus of the suboptimality study is to derive quantities relating the infinite-horizon cost function under the said variant of model predictive control to the respective infinite-horizon value function. The basis control scheme involves usual stabilizing constraints comprising of a terminal set and a terminal cost in the form of a local Lyapunov function. The stage cost is adapted using the principles of Q-learning, a particular approach …
