Discrete-time Nonlinear Control Systems Research Articles

Model-free event-triggered resilient control for discrete-time nonlinear systems under sparse actuator attacks via GrHDP

Model-free event-triggered resilient control for discrete-time nonlinear systems under sparse actuator attacks via GrHDP

Self-organizing neural intelligent control for nonlinear discrete-time systems with particle swarm optimization

Self-organizing neural intelligent control for nonlinear discrete-time systems with particle swarm optimization

A novel intelligent control of discrete-time nonlinear systems in the presence of output saturation

In this paper, a model free control method for a class of discrete time nonlinear systems is introduced. A type-3 fuzzy system estimates the unknown parameters required by the control system. The control system only uses the input and output data of the plant and therefore does not need to know its mathematical equations. On the other hand, the phenomenon of output saturation is a challenging problem for all control systems, addressed in detail in the proposed method. The convergence of the proposed method is guaranteed, and the control system is very robust in the face of changes in the dynamics of the plant. The simulation results on discrete-time nonlinear systems show that the proposed method is very accurate despite the high speed of convergence. In addition, the proposed method is robust for modeling uncertainties and has a better root mean square error and step response time compared to the other methods. Also, a comparison has been made between type-1 to type-3 fuzzy systems and control system based on trial and error, which shows firstly the importance of the presence of fuzzy system and secondly the superiority of type-3 fuzzy system compared to the other two types.

Positive semi-definite Lyapunov function-based adaptive control for nonlinear discrete-time systems with application to chaotic Duffing oscillator

Positive semi-definite Lyapunov function-based adaptive control for nonlinear discrete-time systems with application to chaotic Duffing oscillator

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.

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.

Disturbance Observer Dynamic Linearization-Based Model-Free Adaptive Control for Discrete-Time Nonlinear Systems.

In this article, a disturbance observer dynamic linearization (DL)-based model-free adaptive control (MFAC) scheme is proposed for discrete-time nonlinear systems with disturbances and uncertainties. The partial-form-dynamic-linearization-based disturbance observer (PDO) is constructed by applying the DL method to an unknown ideal disturbance observer. An adaptive updating algorithm of the observer gain is derived by minimizing a estimation criterion function. Then, the PDO-based MFAC scheme is formed and its bounded stability is rigorously analyzed using the contraction mapping principle. The proposed scheme is a purely data-driven control method, that is, both the PDO and control system are designed by using only the input/output data of underlying system. A numerical simulation and a vehicle turning experiment are given to verify the effectiveness of the proposed scheme.

Algebraic Conditions for Accessibility of Discrete-Time Nonlinear Control Systems

Algebraic Conditions for Accessibility of Discrete-Time Nonlinear Control Systems

Control Synthesis for Discrete-Time Nonlinear Control Systems under State and Input Constraints

Control Synthesis for Discrete-Time Nonlinear Control Systems under State and Input Constraints

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.