Discrete-time Nonlinear Control Systems Research Articles

Stabilizing value iteration Q-learning for online evolving control of discrete-time nonlinear systems

Stabilizing value iteration Q-learning for online evolving control of discrete-time nonlinear systems

Constrained-Cost Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems.

For discrete-time nonlinear systems, this research is concerned with optimal control problems (OCPs) with constrained cost, and a novel value iteration with constrained cost (VICC) method is developed to solve the optimal control law with the constrained cost functions. The VICC method is initialized through a value function constructed by a feasible control law. It is proven that the iterative value function is nonincreasing and converges to the solution of the Bellman equation with constrained cost. The feasibility of the iterative control law is proven. The method to find the initial feasible control law is given. Implementation using neural networks (NNs) is introduced, and the convergence is proven by considering the approximation error. Finally, the property of the present VICC method is shown by two simulation examples.

Supplementary Control for Quantized Discrete-Time Nonlinear Systems Under Goal Representation Heuristic Dynamic Programming.

This article is concerned with supplementary control of discrete-time nonlinear systems with multiple controllers in the framework of goal representation heuristic dynamic programming (GrHDP), where a logarithmic quantizer is used to govern the network communication. For the addressed problem, a neural network (NN)-based observer is first proposed to estimate the unknown system state in the simultaneous presence of quantized influence. In light of the estimated states and the ideal control inputs via a zero-sum game, a GrHDP algorithm with a reinforced term is developed to implement the supplementary control task, where some novel weight updating rules are constructed by virtue of an additional tunable parameter to improve the system performance. Furthermore, a set of conditions about the stability of estimated error dynamics of both observer states and updated NNs' weights are derived by resorting to the Lyapunov stability theory. Finally, the effectiveness of the developed method is verified by a power system and a numerical experiment.

Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems With Trajectory-Based Initial Control Policy

Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems With Trajectory-Based Initial Control Policy

Adaptive time-varying state safety constraint control for discrete-time nonlinear systems with random actuator failures

This work investigates the adaptive time-varying state safety constraint control problem for a class of discrete-time nonlinear systems subject to large parameter uncertainties and stochastic actuator failures for the first time. The existence of time-varying full-state constraints, large parameter uncertainties and stochastic actuator failures leads to a series of difficulties for realizing all control objectives. Due to the absence of the linearity property of the derivative in discrete-time log type barrier Lyapunov functions, they are not used to deal with the state constraint problem of nonlinear discrete-time systems. The discrete quadratic-fraction time-varying barrier Lyapunov function is employed to guarantee that all states are constrained in the time-varying predefined regions. By virtue of the constructed multiple-model set, an adaptive identification algorithm is developed to deal with large parameter uncertainties and it has a clear advantage that this method does not requires cn (where n is the dimension of the parameter vector and c is an integer) identification models and only relies on n+1 identification models, thereby heavily reducing the computational burden. By employing the discrete-time filter and backstepping techniques, the adaptive failure compensation controller is designed to ensure the boundedness in probability of the considered systems with respect to stochastic actuator failures. Finally, the effectiveness of the proposed scheme is proved by two simulation examples.

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.

Costate-Supplement ADP for Model-Free Optimal Control of Discrete-Time Nonlinear Systems.

In this article, an adaptive dynamic programming (ADP) scheme utilizing a costate function is proposed for optimal control of unknown discrete-time nonlinear systems. The state-action data are obtained by interacting with the environment under the iterative scheme without any model information. In contrast with the traditional ADP scheme, the collected data in the proposed algorithm are generated with different policies, which improves data utilization in the learning process. In order to approximate the cost function more accurately and to achieve a better policy improvement direction in the case of insufficient data, a separate costate network is introduced to approximate the costate function under the actor-critic framework, and the costate is utilized as supplement information to estimate the cost function more precisely. Furthermore, convergence properties of the proposed algorithm are analyzed to demonstrate that the costate function plays a positive role in the convergence process of the cost function based on the alternate iteration mode of the costate function and cost function under a mild assumption. The uniformly ultimately bounded (UUB) property of all the variables is proven by using the Lyapunov approach. Finally, two numerical examples are presented to demonstrate the effectiveness and computation efficiency of the proposed method.

Convergence and Stability of Optimal Regulation via Generalized N -Step Value Gradient Learning.

In this article, the generalized N -step value gradient learning (GNSVGL) algorithm, which takes a long-term prediction parameter λ into account, is developed for infinite horizon discounted near-optimal control of discrete-time nonlinear systems. The proposed GNSVGL algorithm can accelerate the learning process of adaptive dynamic programming (ADP) and has a better performance by learning from more than one future reward. Compared with the traditional N -step value gradient learning (NSVGL) algorithm with zero initial functions, the proposed GNSVGL algorithm is initialized with positive definite functions. Considering different initial cost functions, the convergence analysis of the value-iteration-based algorithm is provided. The stability condition for the iterative control policy is established to determine the value of the iteration index, under which the control law can make the system asymptotically stable. Under such a condition, if the system is asymptotically stable at the current iteration, then the iterative control laws after this step are guaranteed to be stabilizing. Two critic neural networks and one action network are constructed to approximate the one-return costate function, the λ -return costate function, and the control law, respectively. It is emphasized that one-return and λ -return critic networks are combined to train the action neural network. Finally, via conducting simulation studies and comparisons, the superiority of the developed algorithm is confirmed.

Error-based adaptive optimal tracking control of nonlinear discrete-time systems

Error-based adaptive optimal tracking control of nonlinear discrete-time systems

Neural network optimal control for discrete-time nonlinear systems with known internal dynamics

Neural network optimal control for discrete-time nonlinear systems with known internal dynamics

Finite-Time Model-Free Adaptive Control for Discrete-Time Nonlinear Systems

This paper addresses the fast trajectory tracking problem for discrete-time nonlinear systems, and whereby a finite-time model-free adaptive control (FMFAC) approach is innovatively devised. Here, the nonlinear systems’ dynamics are completely unknown and the widespread disturbances are considered. The nonparametric dynamic linearization technique and the adaptive extended disturbance observer are firstly deployed to achieve real-time linearization of the discrete-time nonlinear system, and an efficient finite-time performance index function is thereafter devised, and thereby contributing to a novel FMFAC control scheme. Theoretical analysis indicates the finite-time model-free tracking control within a stable region can be guaranteed, and the boundedness of the control input signal can be ensured rigorously, even though under the effect of various disturbances. The key points of the proposed FMFAC approach are model-free and possessing the fast regulation ability, and the corresponding effectiveness and superiority are validated via simulation studies.

Nonsmooth funnel function-based model-free adaptive sliding-mode control for discrete-time nonlinear systems

This paper proposes a nonsmooth funnel function (NFF)-based model-free adaptive sliding-mode control strategy for the discrete-time nonlinear systems with unknown dynamics and asymmetric constraints. The dynamic linearization model of the nonlinear systems with unknown dynamics is obtained online only using the input/output data, which is combining with the designed NFF-based discrete-time sliding-mode surface to guarantee asymmetric constraints of the tracking error. In the proposed NFF, the coordinate transformation for asymmetric constraints simplifies the controller design, and the nonsmooth parameter can improve the transient and steady-state performances of the tracking error. The control consumption is further reduced by a proposed time-varying weighting factor-based cost function in the controller design. Furthermore, parameter selections of performance boundaries and the sliding-mode surface are given, and the performance margin (the minimum distance from the tracking error to the preset boundaries) is proved theoretically. Simulation and experimental results verify the effectiveness of the proposed control strategy.

Design of Photovoltaic Power Generation Servo System Based on Discrete Adaptive Network Dynamic Surface Control Technology

In recent years, under the development of the dual carbon goal, the energy crisis has become increasingly serious, and China has also experienced serious power rationing. However, the research on dynamic surface control technology in solar tracking systems in nonlinear control systems is mostly based on continuous-time systems, while adaptive dynamic surface control based on discrete-time nonlinear control systems can describe an actual control system more accurately in the production process. It can effectively suppress interference with extremely high stability and safety. To solve the problem of low efficiency in photovoltaic power generation, this research first built a photovoltaic power generation servo system model based on the parameter of uncertainty. Then, a discrete adaptive neural network dynamic surface (DANNDS) controller was designed to solve the problems in the design of the traditional backstepping method. Finally, based on the designed method of a dynamic surface controller, a discrete adaptive neural network quantization controller (DANNQC) for the photovoltaic power generation servo system was designed by introducing external disturbance. The control parameters and their studied ranges were as follows: The reference signals were or1=sin(0.1t) and or2=cos(0.1t). The parameters of the virtual control law and the final control law were m11=0.01, m22=0.01, m12=0.02, m13=0.02, and m23=0.02. The time constant of the low-pass filter was ζ12=ζ13=ζ22=ζ23=0.005. The parameters of the parameter regulation law were ρ12=ρ13=ρ22=ρ23=0.0005 and a12=a13=20, a22=a23=22. The research results show that the MTE, RMSTE, and 2NTE scores of the height angle servo motor of the DANNDS control method were 0.0026, 7.0279 × 10−4, and 0.3552, respectively. The scores for each index of the azimuth servo motor were 0.0028, 8.9237 × 10−4, and 0.4511, respectively. The height angle tracking error for the DANNQC control method was [−0.02,0.022]. The azimuth tracking error was [−0.03,0.03]. In summary, the photovoltaic power generation servo system based on the DANNQC has a better control performance. By controlling the height angle and azimuth angles, it can better track the position of the sun and adjust the position of the photovoltaic panel in real time. The sun’s rays illuminate the photovoltaic panel at an appropriate angle to achieve maximum power generation efficiency, which is of great practical significance for the development of solar technology.

Observer-based model predictive control for uncertain NCS subject to hybrid attacks via interval type-2 T–S fuzzy model

In this study, an observer-based model predictive control (MPC) algorithm is addressed for an uncertain discrete-time nonlinear networked control system (NCS) subject to hybrid malicious attacks by using interval type-2 Takagi–Sugeno (IT2 T–S) fuzzy theory. Hybrid malicious attacks, including two typical attacks, i.e., denial-of-service (DoS) attacks and false data injection (FDI) attacks, are considered in the communication networks. Under DoS attacks, the control signals will be interfered, which cause the degradation of signal-to-interference-plus-noise ratio, then lead to packets loss. Under FDI attacks, the false signals are injected and output signals are modified so that the system performance is deteriorated. For the NCS subject to hybrid attacks, a secure observer that can resist FDI attacks is devised and a fuzzy MPC algorithm that can solve the controller gains is proposed. Besides, by updating the bound of augmented estimation error, the recursive feasibility can be guaranteed. Finally, illustrative examples are given to show the effectiveness of proposed scheme.

A novel event-triggered constrained control for nonlinear discrete-time systems

<abstract><p>In this paper, a novel event-triggered optimal control method is developed for nonlinear discrete-time systems with constrained inputs. First, a non-quadratic utility function is constructed to overcome the challenge caused by saturating actuators. Second, a novel triggering condition is designed to reduce computational burden. Difference from other triggering conditions, fewer assumptions are required to guarantee asymptotic stability. Then, the optimal cost function and control law are obtained by constructing the action-critic network. Convergence analysis of the system is provided in the consideration of the system state and neural network weight estimation errors. Finally, the effectiveness and correctness of the proposed method are verified by two numerical examples.</p></abstract>

State-Space Region-Invariance of Discrete-Time Control Systems

In the paper, the so called region-invariance properties of discrete-time control systems are considered. An already known notion of positivity of control systems has been generalized (using a kind of geometric insight instead of a pure algebraic approach) to the general nonlinear discrete-time control systems, general regions in state-space, and controls from polyhedral cones in input-space. The class of such control systems has been characterized. Numerous numerical examples illustrating individual cases under consideration are presented in the paper.

Robust Learning-Based Predictive Control for Discrete-Time Nonlinear Systems With Unknown Dynamics and State Constraints

Robust model predictive control (MPC) is a well-known control technique for model-based control with constraints and uncertainties. In classic robust tube-based MPC approaches, an open-loop control sequence is computed via periodically solving an online nominal MPC problem, which requires prior model information and frequent access to onboard computational resources. In this paper, we propose an efficient robust MPC solution based on receding horizon reinforcement learning, called r-LPC, for unknown nonlinear systems with state constraints and disturbances. The proposed r-LPC utilizes a Koopman operator-based prediction model obtained off-line from pre-collected input-output datasets. Unlike classic tube-based MPC, in each prediction time interval of r-LPC, we use an actor-critic structure to learn a near-optimal feedback control policy rather than a control sequence. The resulting closed-loop control policy can be learned off-line and deployed online or learned online in an asynchronous way. In the latter case, online learning can be activated whenever necessary; for instance, the safety constraint is violated with the deployed policy. The closed-loop recursive feasibility, robustness, and asymptotic stability are proven under function approximation errors of the actor-critic networks. Simulation and experimental results on two nonlinear systems with unknown dynamics and disturbances have demonstrated that our approach has better or comparable performance when compared with tube-based MPC and LQR, and outperforms a recently developed actor-critic learning approach.

Observer-Based Asynchronous Control of Nonlinear Systems With Dynamic Event-Based Try-Once-Discard Protocol.

This work investigates the observer-based asynchronous control of discrete-time nonlinear systems with network-induced communication constraints. To avoid the data collisions and side effects in a constrained communication channel, a novel dynamic event-based weighted try-once-discard (DEWTOD) protocol is proposed. In contrast to the existing protocols, the DEWTOD scheduling regulates whether the sampling instant to release and which node to transmit the sampling instant simultaneously. In light of a hidden Markov model, the time-varying detection probability matrix is characterized by a polytopic set. By resorting to the polytopic-structured Lyapunov functional, sufficient conditions are derived such that the closed-loop dynamic is mean-square exponentially stable, and the observer-based controller is designed. In the end, two numerical examples are provided to explicate the validity of the attained methodology.

Event-triggered control for discrete-time delay systems

This study focuses on event-triggered control of nonlinear discrete-time systems with time delays. Based on a Lyapunov–Krasovskii type input-to-state stability result, we propose a novel event-triggered control algorithm that works as follows. The control inputs are updated only when a certain measurement error surpasses a dynamical threshold depending on both the system states and the evolution time. Sufficient conditions are established to ensure that the closed-loop system maintains its asymptotic stability. It is shown that the time-dependent portion in the dynamical threshold is essential to derive the lower bound of the times between two consecutive control updates. As a special case of our results, we demonstrate the performance of the designed event-triggering algorithm for a class of linear control systems with time delays. Numerical simulations are provided to demonstrate the effectiveness of our algorithm and theoretical results.

Observer-based sliding mode control for discrete-time nonlinear system with time-varying delay

This work deals with the design observer-based sliding mode control for discrete-time Takagi–Sugeno fuzzy models with time-varying delay and subject to measurement noises. The sliding surface is developed by introducing the state and input vectors to overcome the restrictive assumption in most existing sliding mode control schemes which forces the input matrices of all linear subsystems to be equal. Sufficient stability conditions of the error system and sliding mode dynamics with disturbance attenuation level are developed using the augmented Lyapunov–Krasovskii functional and free-weighting matrix. Finally, a simulation example is presented to demonstrate the efficiency of the proposed results.