Research On Tracking Control Of Nonlinear Systems With Constrained Characteristics

Constraints are commonly encountered in engineering systems because of their safe consideration,actuator physical limits,mechanical design and manufacturing etc.In recent years,the control problems for state and output constrained nonlinear systems have been largely studied.In order to better meet the demand of engineering application and improve the existing nonlinear system theory,it is necessary to further study of the control problem for constrained nonlinear systems.Based on the barrier Lyapunov function in combination with other advanced control strategy,the tracking control problems are investigated for nonlinear systems with state and output constraints in this paper.The main contributions include:1.For a class of pure-feedback nonlinear systems with full state constraints,a tracking controller is constructed via barrier Lyapunov function combined with adaptive control and dynamic surface control.It is shown that all the signals in the closed-loop system are ultimately bounded and the tracking error converges to an adjustable neighborhood of the origin while the full state constraints are never violated.The dynamic surface solves the difficulty on high order differentiability of stabilising functions,simplified the controller design procedure and reduced the control complexity.2.For a class of strict-feedback nonlinear systems subject to asymmetric time-varying full state constraints which include the known system and the scenarios of parametric uncertainties,the tracking control problem is studied based on the time-varying asymmetric barrier Lyapunov function.The high order coupling terms caused by backstepping are canceled through a novel variable substitution for the first time,asymptotic tracking is achieved without violation of any constraints and all signals in the closed-loop system are ultimately bounded.State-constrained systems with input saturation and bounded disturbances are also considered,the tracking error converges to a bounded set around zero.3.For a class of strict-feedback nonlinear systems subject to asymmetric time-varying full state constraints,the tracking control problem is investigated via barrier Lyapunov function based adaptive backstepping control.The mean value theorem is employed to transform a purefeedback system into a strict-feedback structure with non-affine terms.For the transformed system,time-varying asymmetric barrier Lyapunov functions are employed to ensure the timevarying constraints satisfaction.By allowing the barriers to vary with the desired trajectory in time,the initial condition requirements are relaxed efficiently.The presented control scheme can guarantee that all signals in the closed-loop system are ultimately bounded.It is also proved that the tracking error converges to an adjustable neighborhood of the origin even in the presence of disturbance.4.For a class of constrained strict-feedback nonlinear systems which include both full state constraints and time-varying output constraint,the finite time tracking control problem is investigated.Novel (69)-type barrier Lyapunov functions are proposed to ensure the boundedness of output and fictitious state tracking errors.A new tuning function is constructed to eliminate the effect of uncertainties by using the extended finite-time stability condition.It is shown that under the proposed backstepping control scheme the finite-time convergence of system output tracking error to a small set around zero is realized and the full state constraints are not violated.5.For a class of full state-constrained nonlinear systems with completely unknown control coefficients,uncertain time-varying parameters and disturbances,a barrier Lyapunov function based adaptive robust control design method is proposed.Barrier Lyapunov functions are used to ensure that the full state constraints be not violated,under the Nussbaum gain function the unknown control direction is resolved effectively and the boundedness of uncertain time-varying parameters are guaranteed by using the continuous projection algorithm.As shown as the control result,all the closed loop signals are bounded and full state constraints are not violated.Moreover the system output tracking error will converge to an any small neighbourhood of zero through select proper parameters.