317 research outputs found
Adaptive Backstepping Controller Design for Stochastic Jump Systems
In this technical note, we improve the results in a paper by Shi et al., in which problems of stochastic stability and sliding mode control for a class of linear continuous-time systems with stochastic jumps were considered. However, the system considered is switching stochastically between different subsystems, the dynamics of the jump system can not stay on each sliding surface of subsystems forever, therefore, it is difficult to determine whether the closed-loop system is stochastically stable. In this technical note, the backstepping techniques are adopted to overcome the problem in a paper by Shi et al.. The resulting closed-loop system is bounded in probability. It has been shown that the adaptive control problem for the Markovian jump systems is solvable if a set of coupled linear matrix inequalities (LMIs) have solutions. A numerical example is given to show the potential of the proposed techniques
Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching
A more general class of stochastic nonlinear systems with irreducible homogenous Markovian switching are considered in this paper. As preliminaries, the stability criteria and the existence theorem of strong solutions are first presented by using the inequality of mathematic expectation of a Lyapunov function. The state-feedback controller is designed by regarding Markovian switching as constant such that the closed-loop system has a unique solution, and the equilibrium is asymptotically stable in probability in the large. The output-feedback controller is designed based on a quadratic-plus-quartic-form Lyapunov function such that the closed-loop system has a unique solution with the equilibrium being asymptotically stable in probability in the large in the unbiased case and has a unique bounded-in-probability solution in the biased case
Adaptive Backstepping Control for Fractional-Order Nonlinear Systems with External Disturbance and Uncertain Parameters Using Smooth Control
In this paper, we consider controlling a class of single-input-single-output
(SISO) commensurate fractional-order nonlinear systems with parametric
uncertainty and external disturbance. Based on backstepping approach, an
adaptive controller is proposed with adaptive laws that are used to estimate
the unknown system parameters and the bound of unknown disturbance. Instead of
using discontinuous functions such as the function, an
auxiliary function is employed to obtain a smooth control input that is still
able to achieve perfect tracking in the presence of bounded disturbances.
Indeed, global boundedness of all closed-loop signals and asymptotic perfect
tracking of fractional-order system output to a given reference trajectory are
proved by using fractional directed Lyapunov method. To verify the
effectiveness of the proposed control method, simulation examples are
presented.Comment: Accepted by the IEEE Transactions on Systems, Man and Cybernetics:
Systems with Minor Revision
New advances in H∞ control and filtering for nonlinear systems
The main objective of this special issue is to
summarise recent advances in H∞ control and filtering
for nonlinear systems, including time-delay, hybrid and
stochastic systems. The published papers provide new
ideas and approaches, clearly indicating the advances
made in problem statements, methodologies or applications
with respect to the existing results. The special
issue also includes papers focusing on advanced and
non-traditional methods and presenting considerable
novelties in theoretical background or experimental
setup. Some papers present applications to newly
emerging fields, such as network-based control and
estimation
Switching Controller Design for a Class of Markovian Jump Nonlinear Systems Using Stochastic Small-Gain Theorem
Switching controller design for a class of Markovian jump nonlinear systems with unmodeled dynamics is considered in this paper. Based on the differential equation and infinitesimal generator of jump systems, the concept of Jump Input-to-State practical Stability (JISpS) in probability and stochastic Lyapunov stability criterion are put forward. By using backsetpping technology and stochastic small-gain theorem, a switching controller is proposed which ensures JISpS in probability for the jump nonlinear system. A simulation example illustrates the validity of this design
A Fuzzy Logic-based Cascade Control without Actuator Saturation for the Unmanned Underwater Vehicle Trajectory Tracking
An intelligent control strategy is proposed to eliminate the actuator
saturation problem that exists in the trajectory tracking process of unmanned
underwater vehicles (UUV). The control strategy consists of two parts: for the
kinematic modeling part, a fuzzy logic-refined backstepping control is
developed to achieve control velocities within acceptable ranges and errors of
small fluctuations; on the basis of the velocities deducted by the improved
kinematic control, the sliding mode control (SMC) is introduced in the dynamic
modeling to obtain corresponding torques and forces that should be applied to
the vehicle body. With the control velocities computed by the kinematic model
and applied forces derived by the dynamic model, the robustness and accuracy of
the UUV trajectory without actuator saturation can be achieved
Mean-square Exponential Stabilization of Mixed-autonomy Traffic PDE System
Control of mixed-autonomy traffic where Human-driven Vehicles (HVs) and
Autonomous Vehicles (AVs) coexist on the road have gained increasing attention
over the recent decades. This paper addresses the boundary stabilization
problem for mixed traffic on freeways. The traffic dynamics are described by
uncertain coupled hyperbolic partial differential equations (PDEs) with Markov
jumping parameters, which aim to address the distinctive driving strategies
between AVs and HVs. Considering the spacing policies of AVs vary in the mixed
traffic, the stochastic impact area of AVs is governed by a continuous Markov
chain. The interactions between HVs and AVs such as overtaking or lane changing
are mainly induced by the impact areas. Using backstepping design, we develop a
full-state feedback boundary control law to stabilize the deterministic system
(nominal system). Applying Lyapunov analysis, we demonstrate that the nominal
backstepping control law is able to stabilize the traffic system with Markov
jumping parameters, provided the nominal parameters are sufficiently close to
the stochastic ones on average. The mean-square exponential stability
conditions are derived, and the results are validated by numerical simulations
Barrier Lyapunov function-based adaptive fuzzy attitude tracking control for rigid satellite with input delay and output constraint
This paper investigates the adaptive attitude tracking problem for the rigid satellite involving output constraint, input saturation, input time delay, and external disturbance by integrating barrier Lyapunov function (BLF) and prescribed performance control (PPC). In contrast to the existing approaches, the input delay is addressed by Pade approximation, and the actual control input concerning saturation is obtained by utilizing an auxiliary variable that simplifies the controller design with respect to mean value methods or Nussbaum function-based strategies. Due to the implementation of the BLF control, together with an interval notion-based PPC strategy, not only the system output but also the transformed error produced by PPC are constrained. An adaptive fuzzy controller is then constructed and the predesigned constraints for system output and the transformed error will not be violated. In addition, a smooth switch term is imported into the controller such that the finite time convergence for all error variables is guaranteed for a certain case while the singularity problem is avoided. Finally, simulations are provided to show the effectiveness and potential of the proposed new design techniques
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