Adaptive fuzzy decentralized optimal control for interconnected nonlinear systems with unmodeled dynamics via mixed data and event driven method

Exponential small-gain theorem and fault tolerant safe control of interconnected nonlinear systems

Delay-dependent T–S fuzzy control for nonlinear interconnected systems: Using dithers as auxiliaries

The design of decentralized controllers for physically coupled interconnected systems is a challenging task, especially if constraints on the states and inputs must be satisfied. In this work we focus on the design of decentralized controllers for interconnected linear systems subject to nonlinear, homogeneous physical couplings. For the design and the characterization of controlled invariant regions we exploit the concept of positively invariant family of sets. Basically we utilize in the analysis and design a dynamically varying upper bound for the interconnections between the subsystems. This allows to overcome some conservatism related to existing design approaches. As shown, the controller synthesis can be formulated as loosely coupled LMI feasibility problems. This conceptually allows us to decompose the design into as series of smaller subproblems, which are computationally attractive. We obtain for the coupled nonlinear systems suitable decentralized linear control laws, as well as a family of ellipsoidal sets for which satisfaction of the state and input constraints, as well as positive invariance can be guaranteed. The application of the approach is validated considering the decentralized control of two systems that are interconnected with nonlinear functions.

An efficient method is introduced for solving optimal control and optimal parameter selection problems of nonlinear differential-algebraic systems involving general constraints. These infinite dimensional problems are converted into the finite dimensional optimization problems by using the control parametrization technique. Moreover, the transformed time locations for the control variables are included in such problems. As a result, optimal control problems become acausal optimal parameter selection problems. A modified version of differential evolution is introduced to solve these problems. The integration of the penalty functions is used to ensure the solution onto the feasible domain of the problems. Two industrial systems, a chemical reactor and a robotics arm, are used to illustrate the robustness and effectiveness of the method. The control effects can be improved by selecting the proper time locations as observed from the simulated results.

This article studies the decentralized impulsive control problem for nonlinear interconnected systems (NISs) based on the dynamic event-triggered mechanism. By the fuzzy logic system (FLS)-based backstepping approach, we first propose a dynamic event-triggered impulsive controller. Unlike traditional event-triggered control (ETC), our impulsive control scheme allows for the instantaneous regulation of system states only at some state-dependent impulse instants, thus avoiding control inputs between two triggering moments. Notably, the resulting closed-loop impulsive systems include hybrid dynamics, general nonlinear characteristics, and prescribed performance constraints simultaneously. Based on the Lyapunov analysis method, we prove that even under discrete impulsive controllers, all closed-loop states remain bounded, and the prescribed tracking performance is achieved, namely, the tracking error can converge to a prescribed bounded region within a desired finite time. Then, the proposed impulsive control approach is further extended to the output-feedback case, under which the impulsive control design is based on the observer states. Finally, we show two simulation examples to validate the effectiveness of impulsive control schemes.

This article presents a new stabilizing control scheme for a class of interconnected nonlinear systems subjected to unmodeled dynamics and immeasurable states. Fuzzy logic systems are applied to approximate the unknown functions, and a fuzzy-based state observer is constructed. The interconnection of the overall system is completely compensated via the cyclic-small-gain condition theorem, and the small-gain theorem is introduced to overcome the unmodeled dynamics in each subsystem. Furthermore, assumptions from prior literature are relaxed, and computing burden is reduced through the design of less adaptive laws. This article proves that under the designed control scheme, the closed-loop systems are controlled to be input-to-state practically stable and that all signals are guaranteed to be semiglobally uniformly ultimately bounded. Finally, this article's simulation section illustrates the effectiveness of the proposed approach through an example derived from a practical system model.

The centralized paradigm of a single controller and a single plant upon which modern control theory is built is no longer applicable to modern cyber-physical systems of interest, such as the power-grid, software defined networks or automated highways systems, as these are all large-scale and spatially distributed. Both the scale and the distributed nature of these systems has motivated the decentralization of control schemes into local sub-controllers that measure, exchange and act on locally available subsets of the globally available system information. This decentralization of control logic leads to different decision makers acting on asymmetric information sets, introduces the need for coordination between them, and perhaps not surprisingly makes the resulting optimal control problem much harder to solve. In fact, shortly after such questions were posed, it was realized that seemingly simple decentralized optimal control problems are computationally intractable to solve, with the Wistenhausen counterexample being a famous instance of this phenomenon. Spurred on by this perhaps discouraging result, a concerted 40 year effort to identify tractable classes of distributed optimal control problems culminated in the notion of quadratic invariance, which loosely states that if sub-controllers can exchange information with each other at least as quickly as the effect of their control actions propagates through the plant, then the resulting distributed optimal control problem admits a convex formulation. The identification of quadratic invariance as an appropriate means of convexifying distributed optimal control problems led to a renewed enthusiasm in the controller synthesis community, resulting in a rich set of results over the past decade. The contributions of this thesis can be seen as being a part of this broader family of results, with a particular focus on closing the gap between theory and practice by relaxing or removing assumptions made in the traditional distributed optimal control framework. Our contributions are to the foundational theory of distributed optimal control, and fall under three broad categories, namely controller synthesis, architecture design and system identification. We begin by providing two novel controller synthesis algorithms. The first is a solution to the distributed H∞ optimal control problem subject to delay constraints, and provides the only known exact characterization of delay-constrained distributed controllers satisfying an H∞ norm bound. The second is an explicit dynamic programming solution to a two player LQR state-feedback problem with varying delays. Accommodating varying delays represents an important first step in combining distributed optimal control theory with the area of Networked Control Systems that considers lossy channels in the feedback loop. Our next set of results are concerned with controller architecture design. When designing controllers for large-scale systems, the architectural aspects of the controller such as the placement of actuators, sensors, and the communication links between them can no longer be taken as given -- indeed the task of designing this architecture is now as important as the design of the control laws themselves. To address this task, we formulate the Regularization for Design (RFD) framework, which is a unifying computationally tractable approach, based on the model matching framework and atomic norm regularization, for the simultaneous co-design of a structured optimal controller and the architecture needed to implement it. Our final result is a contribution to distributed system identification. Traditional system identification techniques such as subspace identification are not computationally scalable, and destroy rather than leverage any a priori information about the system's interconnection structure. We argue that in the context of system identification, an essential building block of any scalable algorithm is the ability to estimate local dynamics within a large interconnected system. To that end we propose a promising heuristic for identifying the dynamics of a subsystem that is still connected to a large system. We exploit the fact that the transfer function of the local dynamics is low-order, but full-rank, while the transfer function of the global dynamics is high-order, but low-rank, to formulate this separation task as a nuclear norm minimization problem. Finally, we conclude with a brief discussion of future research directions, with a particular emphasis on how to incorporate the results of this thesis, and those of optimal control theory in general, into a broader theory of dynamics, control and optimization in layered architectures.

Quantized adaptive decentralized control for interconnected nonlinear systems with actuator faults

A robust decentralized model reference adaptive control for non-minimum-phase interconnected systems

Adaptive Decentralized Control of Interconnected Nonlinear Systems with Application to Stabilization of Power Systems

Multilevel Adaptive Control of Interconnected Nonlinear Systems: Application to Double Coupled Inverted Pendulums

Adaptive decentralized control of interconnected nonlinear systems

A small-gain approach to inverse optimal adaptive control of nonlinear systems with unmodeled dynamics

This paper investigates the robust optimal control problem of a class of continuous-time, partially linear, interconnected systems. In addition to the dynamic uncertainties resulted from the interconnected dynamic system, unknown bounded disturbances are taken into account throughout the learning process, wherein the system’s dynamics and the disturbances are assumed unknown. These challenges lead the collected online data to be imperfect. In this scenario, traditional data-driven control techniques, such as adaptive dynamic programming (ADP) and robust ADP, encounter a challenge in approximating the optimal control policy precisely due to imperfect data and computational errors. In this paper, a novel data-driven robust policy iteration method is proposed to simultaneously solve the robust optimal control problems. Without relying on the knowledge of the system’s dynamics, the external disturbances or the complete state, the implementation of the proposed method only needs to access the input and partial state information. Based on the small-gain theorem, the notions of strong unboundedness observability and input-to-output stability, it is guaranteed that the learned robust optimal control gain is stabilizing and that the solution of the closed-loop system is uniformly ultimately bounded despite the existence of dynamic uncertainties and unknown external disturbances. The simulation results reveal the efficiency and practicality of the proposed data-driven control method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This work is motivated by the use of reinforcement learning to improve the quality of designing adaptive optimal controllers for engineering applications. Adaptive dynamic programming methods, in particular policy iteration (PI), are widely used in solving optimal control problems. However, due to the iterative nature of PI, the approximated optimal control policy may be inaccurate and imprecise. Especially, when using imperfect system’s measurements instead of the modelling information. This can result in causing the learned control policy to deviate from the actual optimal policy. This becomes more challenging in the existence of dynamic uncertainties and unknown external disturbances which corrupt the measurements and result in imperfect data. This work investigates the conditions on the uncertainties such that the proposed novel data-driven PI algorithm is robust to system’s uncertainties, unknown external disturbances and imperfect measurements. The approximated robust optimal control policy performs robustly in the existences of imperfect data and uncertainties, and at the same time is close enough to the optimal control policy.

This article studies the problem of adaptive fuzzy fixed-time decentralized control for nonlinear interconnected systems with stochastic disturbances and unknown nonlinearities. In control design, fuzzy logic systems are utilized to identify the unknown nonlinear functions. Combining stochastic fixed-time Lyapunov stability theory with adaptive backstepping control technique, a fuzzy adaptive fixed-time decentralized control design algorithm is developed by adopting smooth projection operator. It is proved that all the state variables of the closed-loop system are globally fixed-time stable in probability. Finally, both numerical and practical examples are provided to elucidate the feasibility of the proposed control algorithm.