Certainty Equivalence Principle Research Articles

Adaptive Consensus of Nonlinearly Parameterized Multi-Agent Systems

This letter studies the distributed adaptive consensus problem for multi-agent systems (MASs) subject to nonlinearly parameterized uncertainties. In the existing research, an adaptive consensus scheme was developed for the same scenario but under the assumption that the uncertainties must be linearly parameterized in their unknown parameters. In this letter, the assumption is removed by using a novel distributed adaptive update law, which makes the scheme applicable for more general nonlinear MASs. This letter contains a general design paradigm using the certainty equivalence principle and specific implementation of it on nonlinear second-order MASs. The results are supported by rigorous mathematical analysis and numerical simulation.

Flight Control for UAV Loitering Over a Ground Target With Unknown Maneuver

This paper proposes a flight controller for an unmanned aerial vehicle (UAV) to loiter over a ground moving target (GMT). We are concerned with the scenario that the stochastically time-varying maneuver of the GMT is unknown to the UAV, which renders it challenging to estimate the GMT's motion state. Assuming that the state of the GMT is available, we first design a discrete-time Lyapunov vector field for the loitering guidance and then design a discrete-time integral sliding mode control (ISMC) to track the guidance commands. By modeling the maneuver process as a finite-state Markov chain, we propose a Rao-Blackwellised particle filter (RBPF), which only requires a few number of particles, to simultaneously estimate the motion state and the maneuver of the GMT with a camera or radar sensor. Then, we apply the principle of certainty equivalence to the ISMC and obtain the flight controller for completing the loitering task. Finally, the effectiveness and advantages of our controller are validated via simulations.

Decentralized adaptive consensus control for discrete‐time heterogeneous semiparametric multiagent systems

SummaryDifferent from the consensus control of traditional multiagent systems, this paper studies the decentralized adaptive consensus control for discrete‐time heterogeneous hidden leader‐following semiparametric multiagent system, in which the dynamic equation of each agent has both parametric uncertainties and nonparametric uncertainties. In the considered system, there is a hidden leader agent who can receive the reference signal, but it can only affect the states of those agents who are in its neighborhood. For other following agents, they do not know the leader's existence or the reference signal, and they can only receive information from their neighbors. Our goal is to design decentralized adaptive controllers to make sure that all agents can track the reference signal, and the closed‐loop system achieves consensus in the presence of mutual coupling relations. Due to the existence of both parametric and nonparametric uncertainties in the system, we need to estimate them separately. For the parametric part, we propose a novel dead zone with threshold converging to zero to modify the traditional gradient update law, while for the nonparametric part, we introduce an auxiliary variable including both two uncertainties to facilitate the nonparametric uncertainties compensation. Based on the certainty equivalence principle in adaptive control theory, the decentralized adaptive controller is designed for each agent to make sure that all of them can track the reference signal. Finally, under the proposed control protocol, strict mathematical proofs are given by using Lyapunov theory; then, simulation results are provided to demonstrate the effectiveness of proposed decentralized adaptive controllers.

Decentralised adaptive synchronisation of a class of discrete-time and nonlinearly parametrised coupled multi-agent systems

ABSTRACT In this paper, the adaptive decentralised control problem of the multi-agent system is considered. Each agent is described by a discrete-time nonlinear inverse model with the unknown parameter. The output of each agent has an influence from the history outputs of its neighbour agents. To deal with uncertainty, a projection-type parameter estimation algorithm is adopted to identify parameter. According to the certainty equivalence principle, the local control law of each agent is designed only using the history outputs of its own and neighbour agents. Under the parameter update law and the local dual control, it is shown that the output of each agent tracks the average value of history outputs from its neighbour agents, and the closed-loop system eventually achieves strong synchronisation. Finally, two simulations for an example are provided to illustrated the validity of the results.

Certainty equivalence principle in stochastic differential games: An inverse problem approach

SummaryThis paper aims to characterize a class of stochastic differential games, which satisfy the certainty equivalence principle beyond the cases with quadratic, linear, or logarithmic value functions. We focus on scalar games with linear dynamics in the players' strategies and with separable payoff functionals. Our results are based on the resolution of an inverse problem that determines strictly concave utility functions of the players so that the game satisfies the certainty equivalence principle. Besides establishing necessary and sufficient conditions, the results obtained in this paper are also a tool for discovering new closed‐form solutions, as we show in two specific applications: in a generalization of a dynamic advertising model and in a game of noncooperative exploitation of a productive asset.

A Distributed Observer for a Class of Nonlinear Systems and Its Application to a Leader-Following Consensus Problem

In this note, we first present a framework for designing a distributed control law to solve a cooperative control problem of nonlinear multiagent systems with a nonlinear leader system. The distributed control law is composed of a purely decentralized control law and a distributed observer for the leader system, based on the certainty equivalence principle. Then, we establish a sufficient condition to guarantee the existence of a distributed observer for a class of nonlinear autonomous systems. The framework is then applied to solve the leader-following consensus problem for a class of high-order nonlinear heterogeneous multiagent systems subject to external disturbances. Our design is illustrated by an example with the Van der Pol system as the leader system.

An output-based distributed observer and its application to the cooperative linear output regulation problem

In this paper, we first extend an existing stability result for a class of linear switched systems. This extended result will relax the existence conditions of the output-based distributed observer for a leader system subject to jointly connected switching communication networks in the literature. As an application of this output-based distributed observer, we solve the cooperative output regulation problem of a linear multi-agent system subject to jointly connected switching communication networks by composing a purely decentralized control law and the output-based distributed observer based on the certainty equivalence principle.

Adaptive Leader-Following Consensus for Multiple Euler-Lagrange Systems With an Uncertain Leader System.

In this paper, we study the leader-following consensus problem of multiple Euler-Lagrange (EL) systems subject to an uncertain leader system. We first establish an adaptive distributed observer for a neutrally stable linear leader system whose system matrix is not known exactly. Under standard assumptions, this adaptive distributed observer can estimate and pass the leader's state to each follower through the communication network of the system without knowing the leader's system matrix exactly. Under the additional assumption that the leader's state is persistently exciting, this adaptive distributed observer can also asymptotically learn the parameters of the leader's system matrix. On the basis of this adaptive distributed observer, we further synthesize an adaptive distributed control law to solve our problem via the certainty equivalence principle. Our result allows the leader-following consensus problem of multiple EL systems to be solved even if none of the followers knows the system matrix of the leader system exactly.

Position‐sensorless adaptive positioning control system for IPMSMs

Position-sensorless positioning control system of interior permanent magnet synchronous motors (IPMSMs) has been energetically researched for high reliability and cost reduction. To achieve fast response of positioning servo systems, accurate parameters of IPMSMs are required. The parameters vary due to temperature and/or ageing, which results in degradation of the positioning control performance. Thus, this study proposes a position-sensorless adaptive positioning control system for IPMSMs using the dynamic certainty equivalence principle for stable parameter identification. In addition, comb filters are used for fast estimation instead of low-pass filters. Experiments are demonstrated to validate the effectiveness and the feasibility of the proposed method.

PAIRS TRADING UNDER DRIFT UNCERTAINTY AND RISK PENALIZATION

In this work, we study a dynamic portfolio optimization problem related to pairs trading, which is an investment strategy that matches a long position in one security with a short position in another security with similar characteristics. The relationship between pairs, called a spread, is modeled by a Gaussian mean-reverting process whose drift rate is modulated by an unobservable continuous-time, finite-state Markov chain. Using the classical stochastic filtering theory, we reduce this problem with partial information to an equivalent one with full information and solve it for the logarithmic utility function, where the terminal wealth is penalized by the riskiness of the portfolio according to the realized volatility of the wealth process. We characterize optimal dollar-neutral strategies as well as optimal value functions under full and partial information and show that the certainty equivalence principle holds for the optimal portfolio strategy. Finally, we provide a numerical analysis for a toy example with a two-state Markov chain.

Robust output consensus of networked heterogeneous nonlinear systems by distributed output regulation

In this paper, we study the output consensus problem of networked heterogeneous nonlinear systems. In contrast to existing results on similar problems, output consensus of all systems is achieved with some robustness not only to heterogeneous dynamics with uncertainties but also to unreliable network communication in terms of network connectivity and communication delays. In particular, we allow the time-varying network topology and the presence of time-varying communication delays in network, which are among the most challenging issues in cooperative control. To solve the problem, we propose a hierarchical control scheme and design a distributed dynamic output feedback control law by the distributed output regulation approach. The proposed control approach offers great flexibility to incorporate the output regulation approach, the separation principle and the certainty equivalence principle to stability analysis of the closed-loop system, thus setting a stage for systematically studying the robust output consensus problem. By establishing some technical lemmas and resorting to ISS Lyapunov technique, we solve the robust output consensus problem of nonlinear multi-agent systems subject to system uncertainties, jointly connected directed network topologies, and arbitrarily bounded and nonuniform time-varying communication delays.

Leader-following attitude consensus of multiple rigid body systems subject to jointly connected switching networks

The leader-following attitude consensus problem of multiple rigid body systems has been studied by the distributed observer approach. The key assumption in the existing results is that the communication network among the rigid body systems is static and connected. Nevertheless, this assumption is undesirable since, typically, the communication network is time-varying and disconnected from time to time due to changes of the environment or failures of some subsystems. In this paper, we will further study the leader-following attitude consensus problem of multiple rigid body systems subject to a jointly connected switching communication network. This new problem is more challenging than the existing one since a jointly connected switching communication network can be disconnected at every time instant. To overcome the difficulty, we first show that the distributed observer for a nonlinear target system subject to a jointly connected switching communication network exists. Then, we further synthesize a distributed control law utilizing this distributed observer for the multiple rigid body systems. Finally, we show that this distributed control law solves our problem through the argument of the certainty equivalence principle.

Cooperative Output Regulation for a Class of Nonlinear Multi-agent Systems with Unknown Control Directions subject to Switching Networks

This paper studies the cooperative output regulation problem for a class of nonlinear multi-agent systems with unknown control directions subject to jointly connected switching networks. Our approach integrates three techniques, namely, the distributed internal model, the Nussbaum gain technique, and the adaptive distributed observer. As a result, an adaptive distributed control law is synthesized based on the certainty equivalence principle. In contrast with the existing results, our approach leads to the solution of the cooperative output regulation problem for a class of nonlinear multi-agent systems whose control directions are unknown and can be different and whose communication network can be directed and disconnected at every time instant.

Energy Saving and Interference Coordination in HetNets Using Dynamic Programming and CEC

Energy efficiency in cellular networks has gained great relevance due to the increasing power supply demands in new generation heterogeneous network (HetNet). On the other hand, interference coordination is a key aspect in HetNets resource management which directly affects the performance and energy consumption. Although these two aspect are intertwined, they have been studied separately so far. In this paper, we address the joint problem of energy saving and interference coordination in HetNets. We formulate the problem as a finite horizon Markov decision process (MDP) leveraging two facts: the user traffic demands usually follow periodic patterns, and the knowledge and prediction of network load is crucial in order to select efficient network configurations. Quality of Service (QoS) in the network is defined as the ratio of users meeting a requirement specified by the operator, and allows us to account for a minimum QoS requirement by including a constraint in the formulation of the MDP. To address this MDP, we propose an approximate dynamic programming (ADP) algorithm which selects energy efficient farsighted configurations with QoS guarantees achieving near optimal performance. This ADP algorithm is built upon: 1) the certainty equivalent control principle, which simplifies the complexity of the MDP, and 2) machine learning techniques: a neural network and a polynomial regressor which allow us to predict the QoS and the consumption of the network in advance. We evaluate our proposal in a LTE-A network simulator following the 3GPP guidelines, and the results obtained show that a joint control of the energy saving and interference coordination mechanisms results in a notably performance improvement compared to a disjoint control, in terms of both energy savings and QoS guarantees. Moreover, our proposal has the advantage of being adaptable to the operator QoS requirements.

Adaptive LFT control of a civil aircraft with online frequency‐domain parameter estimation

SummaryThis paper describes the application of an indirect linear fractional transformation (LFT)–based state‐space adaptive control scheme to a transport aircraft, within the context of the European project REconfiguration of CONtrol in Flight for Integral Global Upset REcovery. The principle of the scheme is to design and validate off‐line a gain‐scheduled controller, depending on the plant parameters to be estimated, and to combine it online with a model estimator, so as to minimize the onboard computational time and complexity. A modal approach, very classical for the design of a flight control law, is used to directly synthesize the static output feedback LFT controller, depending on the control and stability derivatives, ie, the parameters of the linearized aerodynamic state‐space model to be estimated. Since the gain‐scheduled LFT controller online depends on the parameter estimates instead of the true values, its robustness to transient and asymptotic estimation errors needs to be assessed using μ and integral quadratic constraint analysis techniques. A primary concern being an online implementation, a fully recursive frequency‐domain estimation technique is proposed, with a low online computational burden and the capability to track time‐varying parameters. Full nonlinear simulations along a trajectory validate the good performance properties of the combined estimator and gain‐scheduled flight controller. To some extent, minimal guaranteed stability and performance properties of the adaptive scheme can be ensured by switching to a robust controller when the parameter estimates are not reliable enough, thus bypassing the Certainty Equivalence Principle.

Decentralized adaptive synchronization with bounded identification errors for discrete-time nonlinear multi-agent systems with unknown parameters and unknown high-frequency gains

This paper addresses the challenging problem of decentralized adaptive control for a class of coupled hidden leader-follower multi-agent systems, in which each agent is described by a nonlinearly parameterized uncertain model in discrete time and can interact with its neighbors via the history information from its neighbors. One of the agents is a leader, who knows the desired reference trajectory, while other agents cannot receive the desired reference signal or are unaware of existence of the leader. In order to tackle unknown internal parameters and unknown high-frequency gains, a projection-type parameter estimation algorithm is proposed. Based on the certainty equivalence principle and neighborhood history information, the decentralized adaptive control is designed, under which, the boundedness of identification error is guaranteed with the help of the Lyapunov theory. Under some conditions, it is shown that the multi-agent system eventually achieves synchronization in the presence of strong couplings. Finally, a simulation example is given to support the results of the proposed scheme.

Direct and Indirect Model Reference Adaptive Control for Multivariable Piecewise Affine Systems

This article proposes direct and indirect model reference adaptive control strategies for multivariable piecewise affine systems, which constitute a popular tool to model hybrid systems and approximate nonlinear systems. A chosen reference model, which can be linear or also piecewise affine, describes the desired closed-loop system behavior that is to be achieved by the adaptive controllers for unknown system dynamics. Each subsystem acquires its own set of control gains, which is tuned under careful consideration of the switching behavior. In the indirect approach, the use of dynamic gain adjustment avoids singularities in the certainty equivalence principle. It is shown for both algorithms that the state of the reference model is tracked asymptotically given a common Lyapunov function for the switched reference model is available. Furthermore, parameter convergence in both the direct and indirect approach is proven for sufficiently rich reference signals. Finally, both algorithms are evaluated in numerical simulations and their advantages and disadvantages are discussed.

Super twisting controller-based unified FDI and FTC scheme for air path of diesel engine using the certainty equivalence principle

This paper proposes a combination of higher order sliding mode and adaptive control for unified fault detection and isolation and fault tolerant control (FTC) of the air path of a diesel engine. Current diesel engines are equipped with features such as variable geometry turbochargers (VGT) and exhaust gas recirculation (EGR) for exhaust emission control. Since EGR and VGT systems are present in the exhaust channel, they are strongly coupled and are prone to both structured as well as unstructured faults. The proposed controller detects and estimates the structured faults by means of adaptation laws, designed by making use of the certainty equivalence principle. Fault effects are compensated by repositioning the actuators. This allows relaxation of the boundedness condition of the super twisting algorithm, as sliding mode controller gains are required to dominate the unstructured parts only, which consequently reduces chattering. A nonlinear multi-input multi-output reduced state control-oriented model has been employed for working out the FTC strategy for EGR and VGT actuators. The stability of the overall system has been analysed using the Lyapunov stability criterion. Faults and proposed controllers are simulated using a fully validated industrial scale diesel engine model to establish the effectiveness of the algorithm.

Robust Gradient-Based Adaptive Control of Nonlinearly Parametrized Plants

Most of the contributions in adaptive control literature assume that the system dynamics is linearly parametrizable, and a certainty equivalence principle is exploited to guarantee global stability and asymptotic convergence of tracking error to zero. Although linear-in-the-parameters (LIP) assumption is reasonable for a large class of dynamics, there exists a considerable number of real world systems, involving complex dynamics, where nonlinear parametrizations are inevitable. Previous research has shown that classical gradient-based adaptive designs with the certainty equivalence principle do not perform satisfactorily for nonlinear-in-the-parameter (NLIP) systems, and may, in fact, cause instability in many situations. This letter is an attempt toward addressing this issue by a novel non-certainty equivalence adaptive control design, where the classical gradient-based adaptive algorithm is used to tackle the LIP component of the NLIP dynamics, while a robust compensator, appended to the controller, accounts for the linearization error. The designed controller ensures global uniformly ultimately bounded stability of the error dynamics. Simulation results on a model of biochemical process, involving NLIP dynamics, are provided to validate the theoretical development.

Harvesting selectivity and stochastic recruitment in economic models of age-structured fisheries

We develop the age-structured fishery model by including endogenous harvesting selectivity and stochastic recruitment, as a growing body of fishery ecological evidence suggests these factors to be critical for fisheries management. Optimal harvesting selectivity aims to direct fishing towards age classes that are preferable to catch given information on fish growth, natural mortality, and recruitment in addition to implications on harvesting cost. We analytically show that maximum sustainable yield (MSY) leads to potentially serious and previously unrecognized deviation from economic optimality, as it neglects the dependence of harvesting costs on gear selectivity. We further show that the steady-state population level may fall below the MSY population even with zero discounting and stock-dependent harvesting costs. We quantify our results using empirical data for Baltic cod. Applying the age-structured model with endogenous harvesting selectivity, we find large differences between maximum sustainable yield and the economic optimum, although the classic biomass model suggests that these differences should be unimportant. Stochastic recruitment implies a threefold increase in young age classes, but the stochastic solution can be accurately approximated by the certainty equivalence principle.