Output regulation is a fundamental problem in control theory, extensively studied since the 1970s. Traditionally, research has primarily addressed scenarios where the system model is explicitly known, leaving the problem in the absence of a system model less explored. Leveraging the recent advancements in Willems et al.'s fundamental lemma, data-driven control has emerged as a powerful tool for stabilizing unknown systems. This paper tackles the output regulation problem for unknown single and multi-agent systems (MASs) using noisy data. Previous approaches have attempted to solve data-based output regulation equations (OREs), which are inadequate for achieving zero tracking error with noisy data. To circumvent the need for solving data-based OREs, we propose an internal model-based data-driven controller that reformulates the output regulation problem into a stabilization problem. This method is first applied to linear time-invariant (LTI) systems, demonstrating exact solution capabilities, i.e., zero tracking error, through solving a straightforward data-based linear matrix inequality (LMI). Furthermore, we extend our approach to solve the $k$th-order output regulation problem for nonlinear systems. Extensions to both linear and nonlinear MASs are discussed. Finally, numerical tests validate the effectiveness and correctness of the proposed controllers.
This paper concerns the problem of adaptive output regulation for multivariable nonlinear systems in normal form. We present a regulator employing an adaptive internal model of the exogenous signals based on the theory of nonlinear Luenberger observers. Adaptation is performed by means of discrete-time system identification schemes, in which every algorithm fulfilling some optimality and stability conditions can be used. Practical and approximate regulation results are given relating the prediction capabilities of the identified model to the asymptotic bound on the regulated variables, which b…
This paper deals with the problem of adaptive output regulation for multivariable nonlinear systems by presenting a learning-based adaptive internal model-based design strategy. The approach builds on the recently proposed adaptive internal model design techniques based on the theory of nonlinear Luenberger observers, and the adaptation side is approached as a probabilistic regression problem. In particular, Gaussian process priors are employed to cope with the learning problem. Unlike the previous approaches in the field, here only coarse assumptions about the friend structure are required, m…
In this paper we propose a new design paradigm, which employing a postprocessing internal model unit, to approach the problem of output regulation for a class of multivariable minimum-phase nonlinear systems possessing a partial normal form. Contrary to previous approaches, the proposed regulator handles control inputs of dimension larger than the number of regulated variables, provided that a controllability assumption holds, and can employ additional measurements that need not to vanish at the ideal error-zeroing steady state, but that can be useful for stabilization purposes or to fulfil th…
Motivated by the inadequacy of the existing control strategies for power systems affected by time-varying uncontrolled power injections such as loads and the increasingly widespread renewable energy sources, this paper proposes two control schemes based on the well-known output regulation control methodology. The first one is designed based on the classical output regulation theory and addresses the so-called Load Frequency Control (LFC) problem in presence of time-varying uncontrolled power injections. Then, in order to also minimize the generation costs, we use an approximate output regulati…
In this paper, a novel adaptive optimal control strategy is proposed to achieve the cooperative optimal output regulation of continuous-time linear multi-agent systems based on adaptive dynamic programming (ADP). The proposed method is different from those in the existing literature of ADP and cooperative output regulation in the sense that the knowledge of the exosystem dynamics is not required in the design of the exostate observers for those agents with no direct access to the exosystem. Moreover, an optimal control policy is obtained without the prior knowledge of the modeling information …
Cooperative Control of Parallel Actuators for Linear Robust Output Regulation of Uncertain Linear Minimum-phase Plants
School of Mathematics and Statistics, Fuzhou University（福州大学数学与统计学院）；Guangdong Provincial Key Laboratory of Fully Actuated System Control Theory and Technology, School of Automation and Intelligent Manufacturing, Southern University of Science and Technology（南方科技大学自动化与智能制造学院）
This paper proposes a new single input multiple output power supply by integrating a flyback converter and several buck converters. The flyback converter works as the main regulator, and the buck converters provide series voltage compensation with the aim of tight regulation. A time multiplexing switching scheme is proposed to deliver multiple output voltage levels via a two winding transformer and to eliminate the cross regulation between output channels. This configuration reduces the size of flyback transformer and filter capacitors, and consequently improves the overall form factor. A deta…
In this paper, a novel robust output regulation control framework is proposed for the system subject to noise, modeled disturbance and unmodeled disturbance to seek tracking performance and robustness simultaneously. The output regulation scheme is utilized in the framework to track the reference in the presence of modeled disturbance, and the effect of unmodeled disturbance is reduced by an $\mathcal{H}_\infty$ compensator. The Kalman filter can be also introduced in the stabilization loop to deal with the white noise. Furthermore, the tracking error in the presence/absence of noise and distu…
The paper deals with the problem of output regulation in a "non-equilibrium" context for a special class of multivariable nonlinear systems stabilizable by high-gain feedback. A post-processing internal model design suitable for the multivariable nature of the system, which might have more inputs than regulation errors, is proposed. Uncertainties in the system and exosystem are dealt with by assuming that the ideal steady state input belongs to a certain "class of signals" by which an appropriate model set for the internal model can be derived. The adaptation mechanism for the internal model i…
This study focuses on periodic event-triggered (PET) cooperative output regulation problem for a class of nonlinear multi-agent systems. The key feature of PET mechanism is that event-triggered conditions are required to be monitored only periodically. This approach is beneficial for Zeno behavior exclusion and saving of battery energy of onboard sensors. At first, new PET distributed observers are proposed to estimate the leader information. We show that the estimation error converges to zero exponentially with a known convergence rate under asynchronous PET communication. Second, a novel PET…
This paper deals with the output regulation problem of a linear time-invariant system in the presence of sporadically available measurement streams. A regulator with a continuous intersample injection term is proposed, where the intersample injection is provided by a linear dynamical system and the state of which is reset with the arrival of every new measurement updates. The resulting system is augmented with a timer triggering an instantaneous update of the new measurement and the overall system is then analyzed in a hybrid system framework. With the Lyapunov based stability analysis, we off…
We consider the problem of designing a state feedback control law to achieve nonovershooting tracking for feedback linearisable multiple-input multiple-output nonlinear systems. The reference signal is assumed to be obtained from a linear exosystem. The design method adopts known methods for the nonovershooting tracking of linear systems and extends them to the output regulation of feedback linearisable nonlinear systems. The method accommodates arbitrary initial conditions and offers design choice of the tracking convergence speed.
We investigate the problem of practical output regulation, i.e., to design a controller that brings the system output in the vicinity of a desired target value while keeping the other variables bounded. We consider uncertain systems that are possibly nonlinear and the uncertainty of their linear parts is modeled element-wise through a parametric family of matrix boxes. An optimization-based design procedure is proposed that delivers a continuous-time control and estimates the maximal regulation error. We also analyze an event-triggered emulation of this controller, which can be implemented on …
Distributed Output Regulation for a Class of Nonlinear Multi-Agent Systems with Unknown-Input Leaders
School of Automation, Beijing University of Posts and Telecommunications（北京邮电大学自动化学院）；Key Laboratory of Systems and Control, Institute of Systems Science, Chinese Academy of Sciences（中国科学院系统与控制重点实验室，系统科学研究所）
The paper deals with the problem of output regulation of nonlinear systems by presenting a learning-based adaptive internal model-based design strategy. We borrow from the adaptive internal model design technique recently proposed in [1] and extend it by means of a Gaussian process regressor. The learning-based adaptation is performed by following an "event-triggered" logic so that hybrid tools are used to analyse the resulting closed-loop system. Unlike the approach proposed in [1] where the friend is supposed to belong to a specific finite-dimensional model set, here we only require smoothne…
Politecnico di Milano（米兰理工大学）；Nanyang Technological University（南洋理工大学）；Huazhong University of Science and Technology（华中科技大学）；University of Groningen（格罗宁根大学）
This study considers the problem of periodic event-triggered (PET) cooperative output regulation for a class of linear multi-agent systems. The advantage of the PET output regulation is that the data transmission and triggered condition are only needed to be monitored at discrete sampling instants. It is assumed that only a small number of agents can have access to the system matrix and states of the leader. Meanwhile, the PET mechanism is considered not only in the communication between various agents, but also in the sensor-to-controller and controller-to-actuator transmission channels for e…
We address the output regulation problem for a general class of linear stochastic systems. Specifically, we formulate and solve the ideal full-information and output-feedback problems, obtaining perfect, but non-causal, asymptotic regulation. A characterisation of the problem solvability is deduced. We point out that the ideal problems cannot be solved in practice because they unrealistically require that the Brownian motion affecting the system is available for feedback. Drawing from the ideal solution, we formulate and solve approximate versions of the full-information and output-feedback pr…
This paper investigates the output feedback setpoint regulation control of a reaction-diffusion equation by means of boundary control. The considered reaction-diffusion plant may be open-loop unstable. The proposed control strategy consists of the coupling of a finite-dimensional observer and a PI controller in order to achieve the boundary setpoint regulation control of various system outputs such as the Dirichlet and Neumann traces. In this context, it is shown that the order of the finite-dimensional observer can always be selected large enough, with explicit criterion, to achieve both the …
In this paper we consider the problem of voltage regulation of a proton exchange membrane fuel cell connected to an uncertain load through a boost converter. We show that, in spite of the inherent nonlinearities in the current-voltage behaviour of the fuel cell, the voltage of a fuel cell/boost converter system can be regulated with a simple proportional-integral (PI) action designed following the {Passivity-based Control (PBC) approach. The system under consideration consists of a DC-DC converter interfacing a fuel cell with a resistive load. We show that the output voltage of the converter c…
This paper presents a delay-dependent parameter-varying control design approach to address the automated blood pressure regulation problem in the critical patient resuscitation using closed-loop administration of vasopressors. The mean arterial pressure (MAP) response of a patient subject to the intravenous vasoactive drug treatment is modeled as a linear parameter-varying (LPV) model, where varying model parameters and varying time-delay are considered as scheduling parameters of the system. Parameter-dependent Lyapunov-Krasovskii functionals are used to design an output-feedback dynamic cont…
