Barrier Lyapunov Function Based State-constrained Control for a Class of Nonlinear Systems

Yang

Adaptive Control & Signal

et al. 2022

In this article, we investigate the performance-guaranteed tracking control for Euler-Lagrange (EL) systems subject to input saturation and output constraints.The prescribed performance and output constraints are first considered for EL systems with input saturation. Time-varying barrier Lyapunov function (BLF) is employed to ensure constraint satisfaction. An adaptive control method for EL systems with saturation is put forward by adding a speed transformation into the BLF and designing auxiliary variables to the system. Subsequently, neural network is introduced to compensate for uncertainties of systems. In combination with backstepping technique, it is demonstrated that the controller not only guarantees that the tracking error converges to a preset compact set near zero at a specified decay rate, but also ensures that the output always stays within a given boundary. Simulation results further demonstrate the effectiveness of the proposed control scheme.

Section: Introductionmentioning

confidence: 99%

Prescribed performance control of Euler–Lagrange systems with input saturation and output constraints

Yang

Adaptive Control & Signal

et al. 2022

2021 American Control Conference (ACC)

“…However, this approach is restricted to relative-degree-one constraints, and may lead to chattering behaviors that result from finite-time convergence, as will be shown in this paper. Barrier-Lyapunov functions, as proposed in [19], [17], could also be used, in principle, to implement STL specifications, as they combine (linear) state constraints with convergence.…”

Section: Introductionmentioning

confidence: 99%

High Order Control Lyapunov-Barrier Functions for Temporal Logic Specifications

Xiao

Belta

Cassandras

2021

Recent work has shown that stabilizing an affine control system to a desired state while optimizing a quadratic cost subject to state and control constraints can be reduced to a sequence of Quadratic Programs (QPs) by using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). In our own recent work, we defined High Order CBFs (HOCBFs) for systems and constraints with arbitrary relative degrees. In this paper, in order to accommodate initial states that do not satisfy the state constraints and constraints with arbitrary relative degree, we generalize HOCBFs to High Order Control Lyapunov-Barrier Functions (HOCLBFs). We also show that the proposed HOCLBFs can be used to guarantee the Boolean satisfaction of Signal Temporal Logic (STL) formulae over the state of the system. We illustrate our approach on a safety-critical optimal control problem (OCP) for a unicycle.

“…us, the research about the systems with state constraints is very meaningful and necessary on account of the existence of state constraints which may undermine the stability of the system. In order to tackle the problem of state constraints, some effective control techniques (e.g., model predictive control (MPC) [18,19], reference governors (RGs) [20], one-to-one nonlinear mapping (NM) [21][22][23], and barrier Lyapunov functions (BLFs) [24][25][26][27][28]) have been presented. Due to the fact that MPC and RGs require strong online computing capability to guarantee constraints, this requirement restricts their applications in engineering design.…”

Section: Introductionmentioning

confidence: 99%

“…Although many significant research results on adaptive neural network control for uncertain nonstrict-feedback systems have been obtained in [11][12][13][14][15][16][17], their considered systems did not include unmodeled dynamics or full-state constraints. In [21][22][23][24][25][26][27][28], the effective controllers have been designed for the lower-triangular structure nonlinear systems with state constraints and unmodeled dynamics, but their considered systems did not include state delay and their control methods may be invalid to nonstrict-feedback systems on account of subsystem function which contains the whole state variables. Furthermore, the above-mentioned control methods only obtain asymptotic or exponential stability with infinite time.…”

Section: Introductionmentioning

confidence: 99%

“…(i) In contrast to the existing results reported in [21][22][23][24][25][26][27][28]47] where the control methods have been proposed for nonlinear strict-feedback or purefeedback systems with state or output constraints and unmodeled dynamics, a generalization of the results is proposed for a class of nonstrict-feedback state delay systems with state constraints and unmodeled dynamics of which the subsystem function contains the whole state variables. To the best of authors' knowledge, it is the first time to develop an adaptive DSC method for uncertain nonstrict-feedback state delay systems with state constraints and unmodeled dynamics.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Finite-Time Tracking Control for Nonstrict-Feedback State-Delayed Nonlinear Systems with Full-State Constraints and Unmodeled Dynamics

Yao¹,

Tan²,

Wu³

2020

Complexity

The problem of finite-time tracking control is discussed for a class of uncertain nonstrict-feedback time-varying state delay nonlinear systems with full-state constraints and unmodeled dynamics. Different from traditional finite-control methods, a C 1 smooth finite-time adaptive control framework is introduced by employing a smooth switch between the fractional and cubic form state feedback, so that the desired fast finite-time control performance can be guaranteed. By constructing appropriate Lyapunov-Krasovskii functionals, the uncertain terms produced by time-varying state delays are compensated for and unmodeled dynamics is coped with by introducing a dynamical signal. In order to avoid the inherent problem of “complexity of explosion” in the backstepping-design process, the DSC technology with a novel nonlinear filter is introduced to simplify the structure of the controller. Furthermore, the results show that all the internal error signals are driven to converge into small regions in a finite time, and the full-state constraints are not violated. Simulation results verify the effectiveness of the proposed method.