Control Problem For Systems Research Articles

Optimized bipartite formation control for multiagent systems with obstacle and collision avoidance

This paper considers an optimal bipartite formation control problem for high-order nonlinear multiagent systems (MASs) with the consideration of obstacle/collision avoidance. Contrary to existing literature, the control strategy designed in this paper can render the agents in a bipartite formation to complete the obstacle/collision avoidance tasks without requiring the obstacles to be located on the coordinate axis. To save resources, an identifier-critic-actor-based optimized formation control scheme is designed for MASs. An obstacle/collision avoidance approach based on dynamical systems (DS) is designed for high-order nonlinear MASs. Different from the existing related results, the proposed DS-based obstacle/collision avoidance approach can avoid the phenomenon that the control quantities approach infinity near obstacles or other agents, and eliminate the dependence on global information. Finally, a simulation example is given to validate the proposed control method.

Private bipartite consensus control for multi-agent systems: A hierarchical differential privacy scheme

This paper addresses the differentially private bipartite consensus control problem for general linear discrete-time multi-agent systems (MASs), where the initial states of the agents are the sensitive data to be protected from potential eavesdroppers. In response to the cooperative–competitive relationship among the agents, a novel hierarchical differential privacy mechanism (HDPM) is proposed, which consists of a classifier and a pair of input and output noise injectors. The HDPM and the bipartite consensus controller are co-designed to ensure the ultimate mean-square bipartite consensus while preserving differential privacy. Finally, numerical simulations are conducted to illustrate the effectiveness of the proposed algorithm.

Optimal Robust Control of Nonlinear Systems with Unknown Dynamics via NN Learning with Relaxed Excitation.

This paper presents an adaptive learning structure based on neural networks (NNs) to solve the optimal robust control problem for nonlinear continuous-time systems with unknown dynamics and disturbances. First, a system identifier is introduced to approximate the unknown system matrices and disturbances with the help of NNs and parameter estimation techniques. To obtain the optimal solution of the optimal robust control problem, a critic learning control structure is proposed to compute the approximate controller. Unlike existing identifier-critic NNs learning control methods, novel adaptive tuning laws based on Kreisselmeier's regressor extension and mixing technique are designed to estimate the unknown parameters of the two NNs under relaxed persistence of excitation conditions. Furthermore, theoretical analysis is also given to prove the significant relaxation of the proposed convergence conditions. Finally, effectiveness of the proposed learning approach is demonstrated via a simulation study.

Prescribed performance based data-driven adaptive sliding mode control for discrete-time nonlinear systems

This research explores the control problem of discrete-time nonlinear systems with prescribed performance utilizing the data-driven method. Firstly, the equivalent data model of the system is constructed employing the full-form dynamic linearization technique. Secondly, a novel error transformation function is proposed to transform the constrained tracking error into the unconstrained equivalent error. Subsequently, the new sliding function is established to achieve the original tracking error converges to the predetermined asymmetric domain. In contrast to existing methods, the proposed approach has a more straightforward controller structure. Additionally, the introduction of pade approximation simplifies the theoretical analysis. Finally, the superiority of the proposed scheme is validated through simulation results on the single-link manipulator system.

Prescribed-time leader-following consensus and containment control for second-order multiagent systems with only position measurements

The problems of prescribed-time leader-following consensus and prescribed-time containment control for double-integrator multiagent systems (MASs) with only position measurements are investigated in this paper. An observer-based prescribed-time control protocol is proposed, in which the two groups of observers for estimating the consensus errors of each follower both converge to zero within a specified time. Furthermore, the proposed controller only relies on its own observers and does not need to obtain the data from observers embedded in its neighbor nodes. The sufficient conditions for the MASs to achieve the defined prescribed-time consensus and to fulfill the goal of prescribed-time containment control are, respectively, given. The effectiveness of the proposed control protocol is further verified by computer simulations.

Practical robust fixed-time containment control for multi-agent systems under actuator faults

This article considers a containment control problem for nonlinear multi-agent systems with nonautonomous leaders under directed topology, where each follower may experience various actuator faults and unknown external disturbances. A practical robust fixed-time fault-tolerant controller is proposed that eliminates the adverse effects of disturbances and actuator faults while achieving the containment control objective within a fixed-time. Independent of initial states, a sufficient condition of practical robust fixed-time stabilization is derived, further relaxing the constraint of robust fixed-time stabilization. The combination of sliding-mode control and event-triggered mechanism in this approach provides better control performance. One advantage of this method is that the sliding-mode band size is no longer dependent on the sampling interval but rather on the triggering function. Another advantage is that the resource costs for handling faults are effectively reduced. Additionally, an adaptive boundary layer technique is designed to avoid chattering phenomenon of the discontinuous controller, which utilizes adaptive parameters to autonomously adjust the width of boundary layer. Zeno behavior analysis and a simulated example are also presented.

MRAC-based dynamic consensus of linear systems with biased measurements over directed networks

In this paper we address the dynamic leaderless consensus control problem for generic linear systems (stable, unstable, marginally stable, etc.) interconnected over directed networks and under the influence of biased measurements. Essentially, the control problem consists in redesigning a standard distributed consensus controller which, for each system, relies on own state biased measurements and respective erroneous data received from a set of neighbors. The difficulty in such a scheme resides in the fact that the measurement bias is directly amplified by the control gain so it cannot be handled as an additive external disturbance. Our control design relies, on one hand, on the solution of a Riccati equation and, on the other, on the design of an estimator reminiscent of a model-reference-adaptive control design. The estimator successfully computes a bias estimate and completely compensates for its effect if the bias is constant—indeed, in this case, we establish exponential stability of the consensus manifold and we show that the controller provides robustness with respect to time-varying biases.

Guaranteed cost tracking control of constrained input nonlinear uncertain systems using event-based ADP

This article investigates the guaranteed cost robust tracking control problem of nonlinear systems subjected to input constraint and unmatched uncertainty. The event-based adaptive dynamic programming (ADP) approach is utilized to address this problem. First, the tracking error and reference trajectory are combined to form an augmented uncertain system. Then, by decomposing the uncertainty into the matched and unmatched parts, the original tracking problem is converted into the optimal regulation problem of an auxiliary system. The cost function for the auxiliary system is defined, and the associated Hamilton–Jacobi–Bellman (HJB) equation is solved using a single critic neural network (NN). Moreover, a novel event-triggering rule is formulated, and it is shown that the designed event-based controller guarantees that the tracking error is uniformly ultimately bounded. The derivation of event-based guaranteed cost and its relation with the time-based counterpart is presented. The exclusion of the infamous Zeno behavior is guaranteed. The uniform ultimate boundedness of the critic weight estimation error is shown. Finally, the effectiveness of the proposed event-triggered ADP method is illustrated through simulations of the spring–mass–damper system and Van der Pol’s oscillator with unmatched uncertainty.

Dynamic Event-Triggered Strategy-Based Optimal Control of Modular Robot Manipulator: A Multiplayer Nonzero-Sum Game Perspective.

Due to the limited computing and processing ability of modular robot manipulator (MRM) components, such as sensors and controllers, event-triggered mechanisms are considered a crucial communication paradigm shift in resource constrained applications. Dynamic event-triggered mechanism is developing into a new technology by reason of its higher resource utilization efficiency and more flexible system design requirements than traditional event-triggered. Therefore, an optimal control scheme of multiplayer nonzero-sum game based on dynamic event-triggered is developed for MRM systems with uncertain disturbances. First, dynamic model of the MRM is established according to joint torque feedback technique and model uncertainty is estimated by data-driven-based neural network identifier. In the framework of differential game, the tracking control problem of MRM system is transformed into the optimal control problem for multiplayer nonzero-sum game with the control input of each joint module as the player. Then, the static event-triggered control problem of MRM system is studied based on adaptive dynamic programming algorithm. On this basis, the internal dynamic variable describing the previous state of the system is introduced, and the characteristics of dynamic trigger rule and its relationship with static rule are revealed theoretically. By designing an exponential attenuation signal, the minimum sampling interval of the system is always positive, so that Zeno behavior is excluded. Lyapunov theory proves that the system is asymptotically stable and the experimental results verify the validity of the proposed method.

Minimal time sampled-data controls for the ordinary differential system

In this paper, we design a minimal time optimal control problem for an ordinary differential system with sampled-data controls, and use it to approximate a time optimal control problem for the ordinary differential system with distributed controls. We find connections among this problem, a minimal norm sampled-data control problem and a minimization problem, and obtain some properties on these problems. Based on these, we not only build up error estimates for optimal time and optimal controls between the minimal time sampled-data control problem and the minimal time distributed control problem, in terms of the sampling period, but we also prove that such estimates are optimal in some sense.

Online Adaptive Dynamic Programming for Optimal Self-Learning Control of VTOL Aircraft Systems With Disturbances

In this paper, a novel online adaptive dynamic programming control algorithm is developed to solve optimal control problems for Vertical Take Off and Landing (VTOL) aircraft systems. Considering the input disturbances of the VTOL systems and adding perturbation interference term to the value function, a robust policy iteration-based ADP method will be introduced to obtain the optimal controller with an approximate optimal control approach. The convergence property is developed to ensure the value function converges to a finite neighborhood of the optimal one. The uniform ultimate boundedness (UUB) of the iterative errors will be strictly proved by Lyapunov stability theory. Finally, we will give mathematical simulation results with the developed method. Compared with sliding mode control (SMC) and linear quadratic regulator (LQR) methods, the simulation results illustrate better overall performance of the novel method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —As an effective tool to solve the optimal control problem of complex nonlinear systems, adaptive dynamic programming (ADP) can effectively overcome the computational problems caused by “curse of dimensionality”. VTOL aircraft system is a typical strongly coupled, underactuate, non-minimum phase system, and the sudden random disturbances will make the control task more challenging. Aiming at the particularity of VTOL system, a new online policy iteration-based ADP algorithm is developed to obtain optimal control with an approximate optimal control strategy in this paper. Decoupling and disturbances can be effectively avoided. convergence will be analyzed to make sure the value function converge to a finite neighborhood of the optimal value function. The UUB property of the system will be proved by the Lyapunov approach.

Tracking control problem of nonlinear strict-feedback systems with input nonlinearity: An adaptive neural network dynamic surface control method.

In this work, the tracking control problem for a class of nonlinear strict-feedback systems with input nonlinearity is addressed. In response to the influence of input nonlinearity, an auxiliary control system is constructed to compensate for it. To process unknown nonlinear dynamics, radial basis function neural networks (RBFNNs) are introduced to approximate them, and some adaptive updating control laws are designed to estimate unknown parameters. Furthermore, during the dynamic surface control (DSC) design process, first-order low-pass filters are introduced to solve the complexity explosion problems caused by repeated differentiation. After that, an NN-based adaptive dynamic surface tracking controller is proposed to achieve the tracking control. By applying the proposed controller, it can be guaranteed that not only the output of the system can track the desired trajectory, but also that the tracking error can converge to a small neighborhood of zero, while all signals of the closed-loop system are bounded. Finally, the effectiveness of the proposed controller is verified through two examples.

Functional stability of production processes as control problem of discrete systems with change of state vector dimension

Functional stability of production processes as control problem of discrete systems with change of state vector dimension

Distributed Event-Triggered Control for Power Sharing in Grid-Connected AC Microgrid

The traditional communication method will bring a heavy burden to the grid system in the distributed collaborative control of microgrids. In grid-connected ac microgrid, this paper adopts an event-triggered control method to resolve the power sharing problem and reduce the communication cost. To begin, the problem is stated as the control problem of a leader-follower multiagent system and uses a distributed hierarchical control strategy to solve it. The primary controller uses the internal model principle to control the voltage output. To optimize the secondary controller, this paper not only adopts an event-triggered control strategy for the microgrid based on the Lyapunov principle to control the output of the compensator state, but also carries out relevant theoretical verification and analysis to ensure that each agent can exclude Zeno behavior. Finally, simulation instances are used to verify the usefulness of the studied control algorithm.

Learning Robust Predictive Control: A Spatial-Temporal Game Theoretic Approach.

This article investigates robust predictive control problem for unknown dynamical systems. Since the dynamics unavailability restricts feasibility of model-driven methods, learning robust predictive control (LRPC) framework is developed from the aspect of time consistency. Under feedback-like control causality, the robust predictive control is then reconstructed as spatialbKKtemporal games, and we guarantee stability through time-consistent Nash equilibrium. For gradation clarity, our framework is specified as four-follow contents. First, multistep feedback-like control causality is drawn from time series analysis, and Takens' theorem provides theoretical support from steady-state property. Second, control problem is reconstructed as games, while performance and robustness partition the game into temporal nonzero-sum subgames and spatial zero-sum ones, respectively. Next, multistep reinforcement learning (RL) is designed to solve robust predictive control without system model. Convergence is proven through bounds analysis of oscillatory value functions, and properties of receding horizon are derived from time consistency. Finally, data-driven implementation is given with function approximation, and neural networks are chosen to approximate value functions and feedback-like causality. Weights are estimated with least squares errors. Numerical results verify the effectiveness.

Secure Consensus Control of Multiagent Systems Under DoS Attacks: A Switching-Scheme-Based Active Defense Method.

This article studies the secure consensus control problem of multiagent systems (MASs) with a nonzero input leader subject to denial-of-service (DoS) attacks. The introduction of backup topologies makes it possible for MASs to actively defend against DoS attacks. Subsequently, a novel active defense method consisting of two types of state observers, an adaptive topology switching mechanism, and switching controllers is proposed, which can ensure the leader-follower bound consensus even if DoS attacks hinder the interaction between agents. Within such a defense framework, the switching mechanism, driven by the predefined performance index and designed monitoring function, can automatically search for a healthy communication graph among backup topologies. Concurrently, the observer-based switching control strategy will be modified to match the corresponding topology, in which the universal observer and controller parameters in different topologies are obtained by solving linear matrix inequalities. It should be highlighted that the developed defense scheme not only removes the limitations of existing results on the duration and frequency of DoS attacks but also ensures the same upper bound of consensus error before and after DoS attacks. Finally, several simulation examples for different systems illustrate the efficiency and superiority of the theoretical results.

Decentralized Event-Triggered Tracking Control for Unmatched Interconnected Systems via Particle Swarm Optimization-Based Adaptive Dynamic Programming.

The problem of the large-scale interconnected system (LSIS) control is prevalent in practical engineering and is becoming increasingly complex. In this article, we propose a novel decentralized event-triggered tracking control (ETTC) strategy for a class of continuous-time nonlinear LSIS with unmatched interconnected terms and asymmetric input constraints. First, auxiliary subsystems are established to address the unmatched cross-linking terms. Next, the dynamics states of the tracking error and the exosystem are combined to construct a nominal augmented subsystem. By employing a nonquadratic performance function, the input-constrained decentralized tracking control problem is transformed into an optimal control problem for the nominal augmented subsystem. A group of independent parameters and event-triggered conditions are designed to save communication bandwidth and computational resources. Subsequently, the critic-only adaptive dynamic programming (ADP) method is used to solve the Hamilton-Jacobi-Bellman equation (HJBE) associated with the optimal control problem. To improve training success rate, the weights of the critic neural network (NN) are updated by introducing a particle swarm optimization algorithm (PSOA). The tracking error and the NN weights are proved to be uniformly ultimately bounded (UUB) under the proposed ETTC by using the Lyapunov extension theorem. Finally, the simulation example of an unmatched interconnected system is provided to verify the validity of the proposed decentralized method.

Neural networks-based adaptive command filter control for nonlinear systems with unknown backlash-like hysteresis and its application to single link robot manipulator

&lt;abstract&gt;&lt;p&gt;In this paper, an adaptive neural network control problem for nonstrict-feedback nonlinear systems with an unknown backlash-like hysteresis and bounded disturbance was presented. Radial basis function neural networks (RBFNN) were used to approximate the unknown functions and the problem of the explosion of complexity problem was handled by utilizing the command filter method. Furthermore, the influence of an unknown backlash-like hysteresis input was addressed by approximating an intermediate variable. Based on the backstepping method and the command filter technique, an adaptive neural network controller was designed via the approximation abilities of RBFNN. With the help of the Lyapunov stability theory, the proposed controller ensures that all of the signals in closed-loop systems are bounded and that the tracking error fluctuates close to the origin within a bounded area. Finally, a real-world example based on the single-link manipulator was shown to demonstrate the viability of the presented approach.&lt;/p&gt;&lt;/abstract&gt;

Fault-tolerant Safe Control for Water Networks: An Interconnected Switched System Approach

This paper investigates the fault-tolerant safe control problem in water network systems in the presence of process and actuator faults. Firstly, based on the established watersafe benchmark, the studied water network is modeled as an interconnected switched system, and a fault-tolerant regulation problem is proposed while ensuring the states of the system remain within safe regions. Secondly, based on the stability theories for interconnected and switched systems, considering the worst cases of leakage and pump faults, a proper state-dependent safety-guaranteed switching law and distributed control policies are designed. Thirdly, the stability and safety of the proposed approach are proved in theory. Finally, simulations are conducted to validate the effectiveness of the proposed approach on a benchmark water transport system.

Value functional and optimal feedback control in linear-quadratic optimal control problem for fractional-order system

In this paper, a finite-horizon optimal control problem involving a dynamical system described by a linear Caputo fractional differential equation and a quadratic cost functional is considered. An explicit formula for the value functional is given, which includes a solution of a certain Fredholm integral equation. A step-by-step feedback control procedure for constructing $ \varepsilon $-optimal controls with any accuracy $ \varepsilon &gt; 0 $ is proposed. The basis for obtaining these results is the study of a solution of the associated Hamilton–Jacobi–Bellman equation with so-called fractional coinvariant derivatives.