Input Unmodeled Dynamics Research Articles

Prescribed-time adaptive stabilization of high-order stochastic nonlinear systems with unmodeled dynamics and time-varying powers

<p>In this paper, the control problem of prescribed-time adaptive neural stabilization for a class of non-strict feedback stochastic high-order nonlinear systems with dynamic uncertainty and unknown time-varying powers is discussed. The parameter separation technique, dynamic surface control technique, and dynamic signals were used to eradicate the influences of unknown time-varying powers together with state and input unmodeled dynamics, and to mitigate the computational intricacy of the backstepping. In a non-strict feedback framework, the radial basis function neural networks (RBFNNs) and Young's inequality were deployed to reconstruct the continuous unknown nonlinear functions. Finally, by establishing a new criterion of stochastic prescribed-time stability and introducing a proper bounded control gain function, an adaptive neural prescribed-time state-feedback controller was designed, ensuring that all signals of the closed-loop system were semi-global practical prescribed-time stable in probability. A numerical example and a practical example successfully validated the productivity and superiority of the control scheme.</p>

Distributed adaptive cooperative control via command filters for multi-agent systems including input unmodeled dynamics and sensor faults

This study focuses on the topic of distributed adaptive cooperative tracking control (CTC) for non-strict feedback multi-agent systems (MASs) including input unmodeled dynamics, prescribed performance, sensor faults and unknown control directions. An adaptive neural CTC tactic is raised via command filtered backstepping technique. With the help of the property of Gaussian function, the barriers produced by the non-strict feedback terms and partial sensor faults are handled. Moreover, the prescribed performance on measured synchronization error is considered by designing a finite-time performance function. By introducing normalization signals and adjusting parameters, the problems caused by input unmodeled dynamics are resolved. The compensation signals and normalization signals are integrated into the whole Lyapunov function in the stability analysis. All the variables in the controlled system are turned out to be semi-globally uniformly ultimately bounded (SGUUB). Meanwhile, the synchronization errors never exceed to predefined boundary. A simulation example is employed to confirm the viability of the constructed control method.

Finite‐time adaptive quantized control of stochastic nonstrict‐feedback constrained nonlinear systems with multiple unmodeled dynamics

SummaryIn this article, a finite‐time adaptive quantized dynamic surface control problem is solved for stochastic partially nonaffine nonstrict‐feedback constrained nonlinear systems with multiple unmodeled dynamics. Firstly, a variable energy function is built to handle the stochastic state unmodeled dynamics under nonstrict‐feedback structure, and a normalized signal is employed to process the input unmodeled dynamics. Furthermore, a specific transformation technique is introduced to keep all states in a predefined asymmetric dynamic constrained region. Compared with the existing results, it not only avoids the circular argument, and also relaxes the condition of the constraint function. Then, the nonlinear function is approximated with the linearly parameterized neural networks. Subsequently, in order to make the tracking error reach a steady state in the finite time, with the help of the properties of the Gaussian function and dynamic surface control technique, a novel finite‐time adaptive quantized controller is designed to ensure that all error signals are semi‐globally practical finite‐time stable and all states obey stochastic probabilistic constraints. Numerical simulation examples are provided to verify the theoretical results obtained.

Finite‐time command filter‐based adaptive tracking control for nonstrict feedback nonlinear systems with full‐state restrictions and unmodeled dynamics

AbstractThe finite‐time command filter tracking control for a class of nonstrictly feedback nonlinear systems with unmodeled dynamics and full‐state constraints is investigated in this paper. The hyperbolic tangent function is used as a nonlinear mapping technique to solve the obstacle of the full‐state constraints. A new adaptive finite time control method is proposed through command filtering reverse engineering, and the shortcomings of the dynamic surface control (DSC) method are overcome by the error compensation mechanism. Dynamic signal is designed to handle dynamical uncertain terms. Normalization signal is designed to handle input unmodeled dynamics. Unknown nonlinear functions are approximated by radial basis function neural networks. Based on the Lyapunov stability theory, it is proved that all signals in the closed‐loop system are semi‐globally consistent and finally bounded and the output tracking error converges in finite time. Two numerical examples are utilized to verify the effectiveness of the proposed control approach.

MT‐filters‐based adaptive quantized dynamic surface control of stochastic nonstrict‐feedback nonlinear systems including input unmodeled dynamics

AbstractIn this article, the issue of stochastic adaptive dynamic surface control (DSC) is discussed for stochastic nonstrict‐feedback constrained nonlinear systems with input quantization and input unmodeled dynamics. Linearly parametrized neural networks are used to estimate unknown continuous functions. With the help of MT‐filters, the unmeasurable system states are observed. An auxiliary signal constructed by the property of unmodeled dynamics is utilized to deal with the dynamic uncertain terms. Input‐quantized actuator is considered to possess quantization and unmodeled dynamics. Using the hyperbolic tangent function as invertible change, the output constrained stochastic nonstrict‐feedback system is transformed into a novel stochastic nonstrict‐feedback system without restrictions. Based on quantized DSC technology and the property of Gaussian function, adaptive neural control is developed for the transformed stochastic nonstrict‐feedback system. The output abides by stochastic constraints in probability. By the Lyapunov synthesis approach, all signals in the whole system are proved to be semi‐global uniform ultimate bounded in probability. The restriction condition is not triggered. The obtained theoretical findings are verified by two numerical examples.

Sampled‐data output feedback leader‐following consensus for a class of nonlinear multi‐agent systems with input unmodeled dynamics

AbstractThis investigation focuses on the sampled‐data output feedback consensus problem for a class of second‐order nonlinear multi‐agent systems with uncertain time‐varying control coefficient and input unmodeled dynamics. In the considered multi‐agent system, the nonlinearities are more stronger than those under the Lipschitz condition, and the existence of the uncertain time‐varying control coefficient causes the invalidation of the full‐order observer. Under such situation, the reduced‐order observers are designed, and the filters are introduced to handle the uncertainties of the input unmodeled dynamics. By adopting the backstepping method, the sampled‐data consensus protocols are developed, and by selecting an appropriate Lyapunov function candidate, we can demonstrate that the practical leader‐following consensus can be achieved for the considered multi‐agent system by the developed protocols with the suitable design constants and an allowable sampling period. Finally, the effectiveness of the proposed consensus method is illustrated by two simulation examples.

Adaptive quantised control of uncertain non‐linear systems with state constraints and time‐varying delays

This study proposes an adaptive quantised fuzzy control strategy for a class of non-linear systems with time-varying delay, state constraints, and input unmodelled dynamics. Design difficulties focus on the fact that the input-quantised actuator possesses both unknown control gain and non-linear input unmodelled dynamics, and all the states are required to satisfy state constraints. To remove these obstacles, integral barrier Lyapunov functions combined with Nussbaum functions are designed to deal with the unknown control gains and state constraints, and a quantised controller combined with the normalised signal is developed to tackle the quantised input and input unmodelled dynamics. To avoid the chattering and reduce the quantisation error in a wide scope of the control volume, a novel logarithmic uniform hysteresis quantiser is employed, which has both advantages of the existing uniform quantiser and hysteresis quantiser. Two simulation examples of practical control systems are conducted to demonstrate the effectiveness of the proposed control protocol.

Adaptive quantized DSC of output-constrained uncertain nonlinear systems with quantized input and input unmodeled dynamics

In this paper, an adaptive quantized fuzzy dynamic surface control (DSC) stratergy is investigated for a class of nonlinear systems with input unmodeled dynamics and output constraints. A challenge lies in that the input-quantized actuator is considered to possess both unknown control gain and nonlinear input unmodeled dynamics. By quantized controller design and DSC technique, combining normalized signal, integral Lyapunov functions, Nussbaum functions and the adaptive laws, the obstacle caused by quantization and multiple uncertainties is effectively overcome. The designed novel quantizer has the advantages of both the existing uniform quantizer and hysteresis quantizer, which can avoid the chattering and reduce the quantization error no matter the control volume is large or small. By defining a group of transformation based on a logarithmic one to one mapping, time-varying output constraints is satisfied. It is shown that all the signals are bounded, and the output signal is constrained within the preset range.

Adaptive Quantized Control of Output Feedback Nonlinear Systems With Input Unmodeled Dynamics Based on Backstepping and Small-Gain Method

In this article, an adaptive quantized neural backstepping strategy is investigated for a class of nonlinear systems with input unmodeled dynamics and output constraints based on the small-gain method. A challenge lies in the considered input-quantized actuator possessing both unknown control gain and input unmodeled dynamics, and the application of the small-gain theorem when the system possesses input unmodeled dynamics and the output constraints. By the coordinate transformation of the state variables, the input unmodeled dynamics subsystem is transformed into a suitable form for applying the small-gain theorem. By a logarithmic one to one mapping, the time-varying output constraints are tackled. With these methods, the stability proof based on the small-gain theorem is completed. It is shown that all the signals are bounded, and the output signal is constrained within the preset range.

Adaptive control of pure‐feedback nonlinear systems with full‐state time‐varying constraints and unmodeled dynamics

SummaryThis paper focuses on the problem of adaptive control for a class of pure‐feedback nonlinear systems with full‐state time‐varying constraints and unmodeled dynamics. By introducing a one‐to‐one nonlinear mapping, the constrained pure‐feedback nonlinear system with state and input unmodeled dynamics is transformed into unconstrained pure‐feedback system. The controller design based on the transformed novel system is proposed by using a modified dynamic surface control method. Dynamic signal and normalization signal are designed to handle dynamical uncertain terms and input unmodeled dynamics, respectively. By adding nonnegative normalization signal into the whole Lyapunov function and using the introducing compact set in the stability analysis, all signals in the whole system are proved to be semiglobally uniformly ultimately bounded, and all states can obey the time‐varying constraint conditions. A numerical example is provided to demonstrate the effectiveness of the proposed approach.

A General Dynamic Scaling Based Control Redesign to Handle Input Unmodeled Dynamics in Uncertain Nonlinear Systems

A general class of uncertain nonlinear systems with dynamic input uncertainties (nonlinear input unmodeled dynamics) is considered. While the proposed approach can, in general, be applied to multi-input systems, single-input systems are considered here for simplicity. It is shown that if a nominal control law is available to globally asymptotically stabilize the nominal system (without the input unmodeled dynamics), then a dynamic scaling based redesign of the control law can be performed to achieve global asymptotic stabilization of the system with the input unmodeled dynamics. The proposed control redesign approach is applicable to a wide class of nonlinear systems including triangular and non-triangular structures as long as a set of structural and inequality conditions on the system dynamics is satisfied and yields a global robust output-feedback stabilizing controller.

Adaptive neural control of constrained strict-feedback nonlinear systems with input unmodeled dynamics

In this paper, adaptive neural dynamic surface control(DSC) is developed for a class of constrained strict-feedback nonlinear systems with input unmodeled dynamics. By introducing a one to one nonlinear mapping, the output constrained strict-feedback system in the presence of unmodeled dynamics is transformed into a novel unconstrained strict-feedback system. Neural networks (NNs) are employed to approximate unknown nonlinear continuous functions. A normalization signal and an updating parameter are used to handle the uncertain term which input unmodeled dynamics brings about in the design final step. By adding the normalization signal to the whole Lyapunov function and using the defined compact set in stability analysis, all the signals in the closed-loop system are proved to be semi-globally uniformly ultimately bounded (SGUUB), and output constraint is not violated. Two numerical examples are used to illustrate the effectiveness of the proposed adaptive DSC method in handling input unmodeled dynamics.

Reduced-order K-filters based decentralized fuzzy adaptive control of stochastic large-scale nonlinear systems with stochastic input unmodeled dynamics

This paper addresses a decentralized fuzzy adaptive control scheme for stochastic large-scale systems in the presence of stochastic input unmodeled dynamics, which is a novel problem on the research of unmodeled dynamics. The stochastic nonlinear input unmodeled dynamics is restricted to be stochastic input-to-state stable. We introduce changing supply function to deal with the stochastic input unmodeled dynamics and construct the corresponding small gain condition. Due to partial states unavailable for measurement and control gains unknown, we design reduced-order K-filters to estimate the unmeasurable states only. First type fuzzy systems are adopted to approximate the whole of the black-box functions and the unknown continuous system functions, which can degrade the complexity of calculation and simply the K-filters’ structure. Utilizing the changing supply function, dynamic surface control (DSC) method and Chebyshev’s inequality, a strict stability analysis in probability is made. The analysis shows that the control laws can guarantee all the signals to be semi-globally uniformly ultimately bounded (SGUUB) in mean square or the sense of four-moment. Simulation results illustrate the effectiveness of the approach.

Robust adaptive DSC of directly input‐coupled nonlinear systems with input unmodeled dynamics and time‐varying output constraints

SummaryIn this paper, an adaptive robust dynamic surface control is proposed for a class of uncertain nonlinear interconnected systems with time‐varying output constraints and dynamic input and output coupling. The directly coupled inputs and control inputs are both of nonlinear input unmodeled dynamics. To counteract the instable impact of the nonlinear input unmodeled dynamics, normalization signals are designed on the basis of the convergence rates of their Lyapunov functions. With new state variables and control variables being defined, the real control inputs are obtained through solving the equations of intermediate control laws. The time‐varying constraints on output signals are implemented by introducing asymmetric barrier Lyapunov functions. In addition, dynamic signals and decentralized K‐filters are used to deal with the state unmodeled dynamics and to estimate the unmeasurable states, respectively. By the theoretical analysis, the signals in the closed‐loop system are proved to be semi‐globally uniformly ultimately bounded, and the output constraints are guaranteed simultaneously. A numerical example is provided to show the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.

Adaptive DSC of stochastic non‐linear systems with input unmodelled dynamics

An adaptive dynamic surface control (DSC) method is proposed for a class of stochastic non-linear systems with input and state unmodelled dynamics in this paper. A normalisation signal is introduced to restrict the input unmodelled dynamics. By introducing a non-linear transformation, modified DSC is extended and applied to a class of more general stochastic non-linear systems. By theoretical analysis, it is shown that all the signals in the closed-loop system are bounded in probability. Two simulation examples further demonstrate the effectiveness of the proposed control approach.

Performance recovery of a class of uncertain non-affine systems with unmodelled dynamics: an indirect dynamic inversion method

ABSTRACTThis paper presents an output feedback indirect dynamic inversion (IDI) approach for a class of uncertain nonaffine systems with input unmodelled dynamics. Compared with previous approaches to achieve performance recovery, the proposed method aims at dealing with a broader class of nonaffine-in-control systems with triangular structure. An IDI state feedback law is designed first, in which less knowledge of the model plant is needed compared to earlier approximate dynamic inversion methods, thus yielding more robust performance. After that, an extended high-gain observer is designed to accomplish the task with output feedback. Finally, we prove that the designed IDI controller is equivalent to an adaptive proportional-integral (PI) controller, with respect to both time response equivalence and robustness equivalence. The conclusion implies that for the studied strict-feedback non-affine systems with unmodelled dynamics, there always exits a PI controller to stabilise the systems. The effectiveness and benefits of the designed approach are verified by three examples.

Adaptive finite-time tracking control for a class of switched nonlinear systems with unmodeled dynamics

In this paper, an adaptive tracking control scheme is proposed for a class of switched nonlinear systems with state and input unmodeled dynamics. The unmodeled dynamics are dealt with by introducing a first-order filter and a dynamic signal. K-filters are used to estimate the unmeasured states, and the dynamic surface control (DSC) technique is employed to construct the controller to avoid the explosion problem of complexity. By choosing an appropriate common Lyapunov function, the boundedness of all closed-loop signals is proved, and the tracking error can converge to a small neighborhood of zero in finite time under arbitrary switchings. Finally, a simulation example is provided to show the feasibility and validity of the proposed method.

Adaptive prescribed performance control of output feedback systems including input unmodeled dynamics

In this paper, an adaptive prescribed performance tracking control scheme is investigated for a class of output feedback nonlinear systems with input unmodeled dynamics based on dynamic surface control method. A transformation with respect to tracking error is introduced to implement prescribed performance tracking control. A novel description based on Lyapunov function for unmodeled dynamics is presented to deal with state unmodeled dynamics. The negative impact of nonlinear input unmodeled dynamics is offset by using a normalization signal. With the aid of Nussbaum function, the unknown control gain sign is effectively handled in the controller design. By the theoretical analysis, not only the signals in the closed-loop system are proved to be semi-globally uniformly ultimately bounded, but also the transient tracking performance can be guaranteed. Two simulation examples are provided to show the effectiveness of the proposed approach.

Adaptive output feedback dynamic surface control of stochastic nonlinear systems with state and input unmodeled dynamics

SummaryIn this paper, an adaptive neural output feedback control scheme is investigated for a class of stochastic nonlinear systems with unmeasured states and four kinds of uncertainties including uncertain nonlinear function, dynamic disturbance, input unmodeled dynamics, and stochastic inverse dynamics. The unmeasured states are estimated by K‐filters, and stochastic inverse dynamics is dealt with by constructing a changing supply function. The considered input unmodeled dynamic subsystem possesses nonlinear feature, and a dynamic normalization signal is introduced to counteract the unstable effect produced by the input unmodeled dynamics. Combining dynamic surface control technique with stochastic input‐to‐state stability, small‐gain condition, and Chebyshev's inequality, the designed robust adaptive controller can guarantee that all the signals in the closed‐loop system are bounded in probability, and the error signals are semi‐globally uniformly ultimately bounded in mean square or the sense of four‐moment. Simulation results are provided to verify the effectiveness of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.

Global output‐feedback control of systems with dynamic nonlinear input uncertainties through singular perturbation‐based dynamic scaling

SummaryA general class of uncertain nonlinear systems with dynamic input nonlinearities is considered. The system structure includes a core nominal subsystem of triangular structure with additive uncertain nonlinear functions, coupled uncertain nonlinear appended dynamics, and uncertain nonlinear input unmodeled dynamics. The control design is based on dual controller/observer dynamic high‐gain scaling with an additional dynamic scaling based on a singular perturbation‐like redesign to address the non‐affine and uncertain nature of the input appearance in the system dynamics. The proposed approach yields a constructive global robust adaptive output‐feedback control design that is robust to the dynamic input uncertainties and to uncertain nonlinear functions allowed throughout the system structure. Copyright © 2015 John Wiley & Sons, Ltd.