Global stabilization by output feedback for a class of nonlinear systems with uncertain control coefficients and unmeasured states dependent growth

This paper considers the problem of global stabilization by output feedback for a class of nonlinear systems with uncertain control coefficients and with unmeasured states dependent growth. Mainly due to the uncertain control coefficients, the problem has remained unsolved and its major difficulty stems from the inapplicability of the commonly used high-gain like observer. By introducing an appropriate state transformation and a thoroughly novel observer based on high-gain K-filters, the backstepping design approach is successfully proposed to the output-feedback controller for this class of systems. It is shown that the global asymptotic stability of the closed-loop system can be guaranteed by the appropriate choice of the control parameters.

Adaptive Output-Feedback Stabilization for PDE-ODE Cascaded Systems with Unknown Control Coefficient and Spatially Varying Parameter

This paper investigates the adaptive stabilization for a class of uncertain PDE-ODE cascaded systems. Remarkably, the PDE subsystem allows unknown control coefficient and spatially varying parameter, and only its one boundary value is measurable. This renders the system in question more general and practical, and the control problem more challenging. To solve the problem,an invertible transformation is first introduced to change the system into an observer canonical form,from which a couple of filters are constructed to estimate the unmeasurable states. Then, by adaptive technique and infinite-dimensional backstepping method, an adaptive controller is constructed which guarantees that all states of the resulting closed-loop system are bounded while the original system states converging to zero. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed method.

STATE-FEEDBACK ADAPTIVE STABILIZING CONTROL DESIGN FOR A CLASS OF HIGH-ORDER NONLINEAR SYSTEMS WITH UNKNOWN CONTROL COEFFICIENTS

In this paper, a new approach is successfully addressed to design the state-feedback adaptive stabilizing control law for a class of high-order nonlinear systems in triangular form and with unknown and nonidentical control coefficients, whose stabilizing control has been investigated recently under the knowledge that the lower bounds of the control coefficients are exactly known. In the present paper, without any knowledge of the lower bounds of the control coefficients, based on the adaptive technique and appropriately choosing design parameters, we give the recursive design procedure of the stabilizing control law by utilizing the approach of adding a power integrator together with tuning functions. The state-feedback adaptive control law designed not only preserves the equilibrium at the origin, but also guarantees the global asymptotic stability of the closed-loop states and the uniform boundedness of all the other closed-loop signals.

Adaptive neural control of nonlinear periodic time-varying parameterized mixed-order multi-agent systems with unknown control coefficients

In this paper, we first consider the adaptive leader-following consensus problem for a class of nonlinear parameterized mixedorder multi-agent systems with unknown control coefficients and time-varying disturbance parameters of the same period. Neural networks and Fourier series expansions are used to describe the unknown nonlinear periodic time-varying parameterized function.A distributed control protocol is designed based on adaptive control, matrix theory, and Nussbaum function. The robustness of the distributed control protocol is analyzed by combining the stability analysis theory of closed-loop systems. On this basis, this paper discusses the case of time-varying disturbance parameters with non-identical periods, expanding the application scope of this control protocol. Finally, the effectiveness of the algorithm is verified by a simulation example.

Nonlinear combined forecasting model based on fuzzy adaptive variable weight and its application

In order to enhance forecasting precision of problems about nonlinear time series in a complex industry system,a new nonlinear fuzzy adaptive variable weight combined forecasting model was established by using conceptions of the relative error,the change tendency of the forecasted object,gray basic weight and adaptive control coefficient on the basis of the method of fuzzy variable weight.Based on Visual Basic 6.0 platform,a fuzzy adaptive variable weight combined forecasting and management system was developed.The application results reveal that the forecasting precisions from the new nonlinear combined forecasting model are higher than those of other single combined forecasting models and the combined forecasting and management system is very powerful tool for the required decision in complex industry system.

Evaluation of optimal UPFC allocation for improving transmission capacity

A unified power flow controller(UPFC)combines the advantages of various flexible alternating current transmission system(FACTS)devices into a powerful format.Using a 500 kV power grid,this study evaluates the selection and use of a UPFC to improve transmission capacity.The"UPFC unit capacity control proportionality coefficient"is introduced to quantify the control effect of the UPFC,and an optimal calculation method for the UPFC capacity is presented.Following the proposal of a UPFC site selection process,the data of an existing power grid is used to conduct simulations.The simulation results show that the UPFC has a strong ability to improve transmission capacity,and its use is greatly advantageous.Additionally,by applying the proposed selection method,the control effect and economic benefits of the UPFC can be comprehensively considered during project site selection.These findings have a guiding significance for UPFC site selection in ultra-high voltage power grids.

Robust integral control for a class of nonlinear systems with unknown control coefficients

The robust integral control problem is studied for a class of nonlinear systems with input-to-state stable （ISS） unmodeled dynamics in this paper. It does not require a priori knowledge of the control coefficients. Combining the Nussbaum-type gain technique and the backstepping design, we propose a state feedback controller, which could achieve the global asymptotic tracking for any constant reference signal, irrespective of the unmeasured dynamic disturbance. It is shown that the proposed methodology further extends the existing robust nonlinear integral control results. Simulation results verify the correctness of the theoretical analysis.

NN-based Output Tracking for More General Stochastic Nonlinear Systems with Unknown Control Coefficients

This paper considers the output tracking problem for more general classes of stochastic nonlinear systems with unknown control coefficients and driven by noise of unknown covariance. By utilizing the radial basis function neural network approximation method and backstepping technique, we successfully construct a controller to guarantee the solution process to be bounded in probability.The tracking error signal is 4th-moment semi-globally uniformly ultimately bounded（SGUUB） and can be regulated into a small neighborhood of the origin in probability. A simulation example is given to demonstrate the effectiveness of the control scheme.

Adaptive Stabilization for a Class of Feedforward Systems with Zero-Dynamics

This paper investigates adaptive state feedback stabilization for a class of feedforward nonlinear systems with zero-dynamics, unknown linear growth rate and control coefficient. For design convenience, the state transformation is first introduced and the new system is obtained. Then, the estimation law is constructed for the unknown control coefficient, and the state feedback controller is proposed with a gain updated on-line. By appropriate choice of the estimation law for the control coefficient and the dynamic gain, the states of the closed-loop system are globally bounded, and the state of the original system converges to zero. Finally, a simulation example is given to illustrate the correctness of the theoretical results.

Continuous output-feedback stabilization for a class of stochastic high-order nonlinear systems

This paper is concerned with the global stabilization via output-feedback for a class of high-order stochastic nonlinear systems with unmeasurable states dependent growth and uncertain control coefficients. Indeed, there have been abundant deterministic results which recently inspired the intense investigation for their stochastic analogous. However, because of the possibility of non-unique solutions to the systems, there lack basic concepts and theorems for the problem under investigation. First of all, two stochastic stability concepts are generalized to allow the stochastic systems with more than one solution, and a key theorem is given to provide the sufficient conditions for the stochastic stabilities in a weaker sense. Then, by introducing the suitable reduced order observer and appropriate control Lyapunov functions, and by using the method of adding a power integrator, a continuous （nonsmooth） output-feedback controller is successfully designed, which guarantees that the closed-loop system is globally asymptotically stable in probability.