Non-affine Input Research Articles

Adaptive performance optimal control for flexible-joint robots with random noises: Design and experiment

This study developes a flexible performance optimal control scheme via reinforcement learning strategy and event-triggered mechanism for flexible-joint robots with random noise and non-affine input. It is notable that an event-triggered optimization mechanism is developed, which meets the optimality principle and saves communication resources. Nevertheless, the existing event-triggered strategy is unable to handle non-affine input, which limits the applicability of this method. To overcome the above problems, a modified event-triggered mechanism is proposed. At the same time, the optimal solution of the system is given by an optimized control algorithm based on the improved performance index function. In the controller design, neural network is used to deal with random disturbances and uncertainties, and an adaptive law is designed to replace the identifier structure. Besides, a flexible prescribed performance function is constructed to yield multiple prescribed performance behaviors by adjusting the key parameters, while the tracking error is stayed within a prescribed boundary. Finally, the effectiveness of the proposed control scheme is further demonstrated by simulation and the experiment of the 2-link flexible-joint robot on the Quanser platform.

RL-based adaptive control for a class of non-affine uncertain stochastic systems with mismatched disturbances

This paper investigates the reinforcement learning (RL) adaptive tracking control design problem for a class of mismatched stochastic nonlinear systems with non-affine structure. The stochastic system studied in this paper is more generally representative due to the presence of non-affine inputs, internal uncertainties, and mismatched external disturbances. Firstly, in order to solve the non-affine structure of stochastic systems, an extended stochastic differential equation is constructed. Based on the actor–critic framework, by generating reinforcement signals, the network is stimulated to evolve more quickly towards the desired direction, while compensating internal uncertainties and induced uncertainties in the stochastic system. Furthermore, aiming at the approximation errors and external disturbances, while satisfying stochastic stability, the adaptive laws for disturbances boundary estimator are established with the usage of higher powers of tracking errors. As a result, a novel non-affine adaptive tracking controller has been proposed by integrating RL, disturbances boundary estimation, and dynamic surface method. Through the stability analysis, it is proved that all closed-loop signals are bounded in probability, and the system output converges to a small neighborhood near the desired trajectory. Numerical simulations demonstrate the effectiveness and superiority of the proposed controller.

A New Event-Triggered Adaptive Fixed-Time Control Design for Uncertain Nonlinear Systems.

This article investigates the problem of dynamic memory event-triggered (DMET) fixed-time tracking control within time-varying asymmetric constraints for nonaffine nonstrict-feedback uncertain nonlinear systems with unmodeled dynamics and unknown disturbances. The existing dynamic event-triggered control methods cannot handle the nonlinear systems with unmodeled dynamics and nonaffine inputs, which greatly limits the applicability of the strategy. To this end, a novel DMET adaptive fuzzy fixed-time control protocol is constructed based on the idea of command filtered backstepping, in which a new dynamic signal function is established to deal with the unmodeled dynamics and an improved DMET mechanism (DMETM) is designed to solve the problem of nonaffine inputs. It is proved that the newly DMET control strategy ensures the tracking error converges to an arbitrarily small compact set in a fixed time and all the signals of the closed-loop systems are bounded. The effectiveness of the proposed approach is demonstrated by two simulation examples.

Output constrained neural adaptive control for a class of KKVs with non-affine inputs and unmodeled dynamics

AbstractIn this paper, an adaptive neural output-constrained control algorithm is proposed for a class of non-affine kinetic kill vehicle (KKV) systems. The key point is that the non-affine control law can be designed and the output of the KKV system conform to the output limit with the aid of the proposed method. Due to the aerodynamic moments, the actual control torque is non-affine, which can be addressed by introducing an integral process to the design of the controller. Besides, in order to improve the control precision, a nonlinear mapping is put forward so that the output constraint can be transformed to the constraint of the introduced dynamic signal that can be simply achieved. From the simulation results it can be concluded that the states of the KKV system can track the desired trajectories in spite of different working conditions and the control precision is higher compared with other control methods.

Finite‐time tracking control for nonaffine nonlinear pure‐feedback systems with a prescribed performance

AbstractThis article investigates the finite‐time tracking control problem of nonlinear pure‐feedback systems with nonaffine input signals. By using a low‐pass filter, the nonaffine system is transformed into a pure‐feedback system with an affine input. To characterize the dynamic and steady‐state performance, a new performance function is defined, which is intergraded into adaptive fuzzy rules to design a novel fractional‐power‐based output tracking controller. It is shown that the tracking error converges to a predefined range at a settling time according to the traditional finite‐time stability theory. Simulation results obtained for two examples reveal the effectiveness of the proposed method.

Dynamic inversion-based hysteresis compensation using extended high-gain observer

We consider the tracking problem for an uncertain nonlinear single-input-single-output system satisfying the minimum-phase assumption, preceded by an unknown hysteresis operator. This is a widely used model for smart material-actuated systems, such as piezo-based nanopositioning systems. Existing hysteresis compensation methods typically require explicit hysteresis models, which tend to be high-dimensional operators and entail significant complexity in model identification and inversion. We propose an output feedback-based hysteresis compensation approach for this class of systems using dynamic inversion and extended high-gain observers. With mild assumptions on the hysteresis nonlinearity properties, the system can be represented as an uncertain, nonaffine, nonlinear system containing a hysteretic perturbation. Dynamic inversion is used to deal with the nonaffine input, uncertainties, and the hysteretic perturbation, where the latter two are estimated using an extended high-gain observer. Analysis of the closed-loop system under output feedback shows that the tracking error converges to a small neighborhood near the origin, which can be made arbitrarily small via a proper choice of time-scale parameters of dynamic inversion and the observer, respectively. Simulation results are presented to show the interplay between these two parameters. Finally, experiments conducted on a commercial nanopositioner confirm the theoretical analysis and demonstrate that the proposed method delivers performance comparable to several competing methods, all of which require an explicit hysteresis inversion operator.

Nonaffine Helicopter Control Design and Implementation Based on a Robust Explicit Nonlinear Model Predictive Control

Control design for a helicopter is a challenging problem because of its nonaffine inputs, its underactuated characteristics, and highly coupled dynamics. To solve a control problem of the helicopter under model uncertainties and disturbance present environments, an explicit nonlinear model predictive control (ENMPC), a dynamic inversion (DI), and an extended high-gain observer (EHGO) are combined in a multi-time-scale fashion. The multi-time-scale scaled structure and the ENMPC provide the framework of the control design, the DI deals with nonaffine control inputs, and the EHGO estimates the unmeasured system states and uncertainties. The proposed control design is discretized to be implemented on a small-scale helicopter. The successful outdoor experiments with the proposed control implemented on autopilot hardware demonstrate the validity of our approach in the presence of model uncertainties and wind disturbances.

WITHDRAWN: Deep learning for Koopman Operator Optimal Control

Nonlinear dynamics are ubiquitous in complex systems. Their applications range from robotics to computational neuroscience. In this work, the Koopman framework for globally linearizing nonlinear dynamics is introduced. Under this framework, the nonlinear observable states are lifted into a higher dimensional, linear regime. The challenge is to identify functions that facilitate the coordinate transformation to this raised linear space. This point is tackled using deep learning, where nonlinear dynamics are learned in a model-free manner, i.e., the underlying dynamics are uncovered using data rather than the nonlinear state-space equations. The main contributions include an implementation of the Linearly Recurrent Encoder Network (LREN) that is faster than the existing implementation and is significantly faster than the state-of-the-art deep learning-based approach. Also, a novel architecture termed Deep Encoder with Initial State Parameterization (DENIS) is proposed. By deriving an energy-budget control performance evaluation method, we demonstrate that DENIS also outperforms LREN in control performance. It is also on-par with and sometimes better than the iterative linear quadratic regulator (iLQR), which requires access to the state-space equations. Extensive experiments are done on DENIS to validate its performance. Also, another novel architecture termed Double Encoder for Input Nonaffine systems (DEINA) is described. Additionally, DEINA's potential ability to outperform existing Koopman frameworks for controlling nonaffine input systems is shown. We attribute this to using an auxiliary network to nonlinearly transform the inputs, thereby lifting the strong linear constraints imposed by the traditional Koopman approximation approach. Koopman model predictive control (KMPC) is implemented to verify that our models can also be successfully controlled under this popular approach. Overall, we demonstrate the deep learning-based Koopman framework shows promise for optimally controlling nonlinear dynamics.

Adaptive control of linearly parameterized nonaffine nonlinear systems via dynamic matching

SummaryThis article studies an adaptive control problem for nonaffine nonlinear systems with linear parametric uncertainty. Inspired by the affine system case, the studied nonaffine nonlinear systems are specified such that the ideal control input is implicitly defined by a matching equation stemming from a Lyapunov‐based analysis. The core idea of control design is to solve the matching equation in a dynamic manner. Toward this end, a dynamic state‐feedback law, together with an adaptation law for the unknown parameters, is developed such that global asymptotic stabilization is theoretically guaranteed. The proposed method is validated on a Duffing‐Holmes oscillator with a nonaffine input and a multi‐input numerical example.

Adaptive Regulation of Discrete-Time Nonaffine Systems With Parametric Uncertainty

This article investigates the problem of global adaptive stabilization for discrete-time nonlinearly parameterized systems with nonaffine inputs. Using the notion of passivity and the idea of small bounded feedback, we present a discrete-time adaptive controller that globally adaptively stabilizes a class of nonaffine systems with unknown parameters, under the assumptions that the unforced dynamics are stable and the controllabilitylike rank conditions hold. The latter is shown to be characterizable by the vector fields $f(x,0,\theta)$ and $\frac{\partial f}{\partial u}(x, 0, \theta)$ , together with their “Lie derivatives” and “Lie brackets” in discrete time.

Voltage Regulation of DC-Microgrid With PV and Battery

This paper studies voltage regulation and maximum power point tracking (MPPT) control for a DC-microgrid that includes a photovoltaic (PV) panel, battery, constant resistance and constant power loads. A dynamic model of the DC-microgrid system described by a multi-input and multi-output nonlinear system with non-affine inputs is derived. Based on this nonlinear dynamic model, we use output regulation theory to design a local state feedback controller that regulates voltages to prescribe set points and maximizes PV power output. Global set point regulation is also studied using passive system theory for non-affine systems and Lyapunov stability theory. The effectiveness of the proposed control schemes is investigated using simulations when changes in both illumination and load occur.

System Transformation-Based Neural Control for Full-State-Constrained Pure-Feedback Systems via Disturbance Observer.

In this article, a novel disturbance observer-based adaptive neural control (ANC) scheme is proposed for full-state-constrained pure-feedback nonlinear systems using a new system transformation method. A nonlinear transformation function in a uniformed design framework is constructed to convert the original states with constrained bounds into the ones without any constraints. By combining an auxiliary first-order filter, an augmented nonlinear system without any state constraint is derived to circumvent the difficulty of the controller design caused by the nonaffine input signal. Based on the augmented nonlinear system, a nonlinear disturbance observer (NDO) is designed to enhance the disturbance rejection ability. Subsequently, the NDO-based ANC scheme is presented by combining the second-order filters with backstepping. The proposed scheme confines all states within the predefined bounds, eliminates the condition on both the known sign and bounds of control gains, improves the robustness of the closed-loop system, and alleviates the computational burden. Two simulation examples are performed to show the validity of the presented scheme.

Linear Active Disturbance Rejection Control for Nonaffine Strict-Feedback Nonlinear Systems

This paper presents a linear active disturbance rejection controller (LADRC) for nonaffine nonlinear systems with strict-feedback form. The proposed LADRC results in a closed-loop system with a three-time-scale structure, in which a reduced-order linear extended state observer estimates unmeasured states and total disturbance in the fastest time scale and dynamic inversion based on sector conditions is used to deal with nonaffine inputs in the intermediate time scale while the system dynamics evolves in the slowest time scale. The singular perturbation method is used to analyze the stability and performance of the system. The effectiveness of the proposed LADRC is demonstrated through simulation studies and experimental validation on a linear motor servo system with nonaffine uncertainties.

Voltage Regulation of DC-Microgrid with PV and Battery: A Passivity Method

This paper presents voltage regulation and maximum power point tracking (MPPT) control schemes for a class of DC-microgrids. The DC-microgrid under consideration consists of a photovoltaic (PV) panel, battery, along with constant resistance and constant power loads. In this study, a dynamic model of the DC-microgrid system is derived and described by a multi-input and multi-output nonlinear system with non-affine inputs. Based on the nonlinear model thus built, we design nonlinear controllers that globally regulate voltages to prescribe set points and maximize the power output from PV by virtue of passivity and Lyapunov stability. The effectiveness of the proposed control schemes is validated by simulations.

Adaptive thermal control for PEMFC systems with guaranteed performance

Proton exchange membrane fuel cell (PEMFC) s are faced with dynamical load scenario in practical applications, and the resulting temperature variation will decrease the performance and consequently shorten the fuel cell lifetime. To address this problem, a control strategy for regulating the stack temperature is proposed in this paper. Firstly, a thermal management-oriented dynamic model of a water-cooled PEMFC system is built to facilitate the control design. Secondly, considering that the stack temperature should be maintained in a certain range regardless of the dynamical changing current demand, a Barrier Lyapunov function is employed to construct a feedback error of the stack temperature. Thirdly, a set of adaptation laws is designed to estimate the unknown parameters related to the gas flow rates in the flow fields. Particularly, a dynamic inversion tracking methodology is applied to design the non-affine input. A Lyapunov method based analysis demonstrates the stability and convergence of the closed-loop properties. Simulation results are provided to show that the proposed control strategy can satisfy all the control objectives and enhance the control performance compared to the proportional-integral controlled case.

Adaptive Fuzzy Sliding Mode Control for MIMO Nonaffine Dutch-Roll System

A robust fuzzy sliding mode controller is presented for a multiple-input–multiple-output (MIMO) Dutch-Roll system with nonaffine inputs and external disturbances. An integrating factor with a nonlinear saturation function is introduced to construct a nonlinear integral sliding mode (NISM) surface to provide better transient response than traditional sliding mode control. Fuzzy logic systems are employed to approximate the unknown nonaffine part of the system directly. Based on Lyapunov method, the tracking errors are guaranteed to be asymptotically stable with the additional adaptive compensation terms. To verify the feasibility and effectiveness of the proposed controller, the Dutch-Roll system is presented for simulation.

Output feedback performance recovery in the presence of uncertainties

We propose an output-feedback tracking controller for uncertain, nonaffine, nonlinear systems. The output feedback controller results in a closed-loop system with a three-time-scale structure; an extended high-gain observer estimates unmeasured states and uncertainties in the fastest time scale and dynamic inversion is used to deal with nonaffine inputs and input uncertainties in the intermediate time scale while the plant dynamics evolves in the slowest time scale. The dynamic inversion algorithm is based on sector conditions and results in exponential convergence of the inputs. Together with the extended high-gain observer, dynamic inversion results in performance recovery of a target system. The singular perturbation method is used to analyze the stability and performance of the system and numerical simulations are used to demonstrate the effectiveness of the control design.

Discretization of Nonlinear Non-affine Time Delay Systems Based on Second-order Hold

When calculating the sampled-date representation of nonlinear systems second-order hold (SOH) assumption can be applied to improving the precision of the discretization results. This paper proposes a discretization method based on Taylor series and the SOH assumption for the nonlinear systems with the time delayed non-affine input. The mathematical structure of the proposed discretization method is explored. This proposed discretization method can provide a precise and finite dimensional discretization model for the nonlinear time-delayed non-affine system by keeping the truncation order of the Taylor series. The performance of the proposed discretization method is evaluated by doing the simulation using a nonlinear system with the time-delayed non-affine input. Different input signals, time-delay values and sampling periods are considered in the simulation to investigate the proposed method. The simulation results demonstrate that the proposed method is practical and easy for time-delayed nonlinear non-affine systems. The comparison between SOH assumption with first-order hold (FOH) and zero-order hold (ZOH) assumptions is given to show the advantages of the proposed method.

Approximation of Nonlinear Time Delay Systems with Non-affine Input

Approximation of Nonlinear Time Delay Systems with Non-affine Input

Adaptive fuzzy control for a class of chaotic systems with nonaffine inputs

A robust adaptive fuzzy control scheme is presented for a class of chaotic systems with nonaffine inputs, modeling uncertainties and external disturbances by using backstepping approach. Fuzzy logic systems (FLS) are employed to approximate the unknown parts of the virtual control and practical controls. The main characteristics of the scheme are that the number of the online adaptive parameters is no more than two times of the order of chaotic system and the tracking errors are guaranteed to be uniformly asymptotically stable with the aid of additional adaptive compensation terms. Lorenz system, Chen system, Lü system and Liu system are presented to illustrate the feasibility and effectiveness of the proposed control technique.