Lifelong Learning-Based Multilayer Neural Network Control of Nonlinear Continuous-Time Strict-Feedback Systems

In This Paper, We Investigate Lifelong Learning (LL)-Based Tracking Control for Partially Uncertain Strict Feedback Nonlinear Systems with State Constraints, employing a Singular Value Decomposition (SVD) of the Multilayer Neural Networks (MNNs) Activation Function based Weight Tuning Scheme. the Novel SVD-Based Approach Extends the MNN Weight Tuning to (Formula Presented.) Layers. a Unique Online LL Method, based on Tracking Error, is Integrated into the MNN Weight Update Laws to Counteract Catastrophic Forgetting. to Adeptly Address Constraints for Safety Assurances, Taking into Account the Effects Caused by Disturbances, We Utilize a Time-Varying Barrier Lyapunov Function (TBLF) that Ensures a Uniformly Ultimately Bounded Closed-Loop System. the Effectiveness of the Proposed Safe LL MNN Approach is Demonstrated through a Leader-Follower Formation Scenario Involving Unknown Kinematics and Dynamics. Supporting Simulation Results of Mobile Robot Formation Control Are Provided, Confirming the Theoretical Findings

Adaptive Fuzzy Tracking Control for Nonlinear State Constrained Pure-Feedback Systems With Input Delay via Dynamic Surface Technique

This brief constructs the adaptive backstepping control scheme for a class of pure-feedback systems with input delay and full state constraints. With the help of Mean Value Theorem, the pure-feedback system is transformed into strict-feedback one. Barrier Lyapunov functions are employed to guarantee all of the states remain constrained within predefined sets. By introducing the Pade approximation method and corresponding intermediate, the impact generated by input delay on the output tracking performance of the system can be eliminated. Furthermore, a low-pass filter driven by a newly-defined control input, is employed to generate the actual control input, which facilitates the design of backstepping control. To approximate the unknown functions with a desired level of accuracy, the fuzzy logic systems (FLSs) are utilized by choosing appropriate fuzzy rules, logics and so on. The minimal learning parameter (MLP) technique is employed to decrease the number of nodes and parameters in FLSs, and dynamic surface control (DSC) technique is leveraged to avoid so-called "explosion of complexity". Moreover, smooth robust compensators are introduced to circumvent the influences of external disturbance and approximation errors. By stability analysis, it is proved that all of signals in the closed-loop system are semi-globally ultimately uniform bounded, and the tracking error can be within a arbitrary small neighbor of origin via selecting appropriate parameters of controllers. Finally, the results of numerical illustration are provided to demonstrate the effectiveness of the designed method.Comment: arXiv admin note: text overlap with arXiv:2310.1540

Advanced Computational-Effective Control and Observation Schemes for Constrained Nonlinear Systems

Constraints are one of the most common challenges that must be faced in control systems design. The sources of constraints in engineering applications are several, ranging from actuator saturations to safety restrictions, from imposed operating conditions to trajectory limitations. Their presence cannot be avoided, and their importance grows even more in high performance or hazardous applications. As a consequence, a common strategy to mitigate their negative effect is to oversize the components. This conservative choice could be largely avoided if the controller was designed taking all limitations into account. Similarly, neglecting the constraints in system estimation often leads to suboptimal solutions, which in turn may negatively affect the control effectiveness. Therefore, with the idea of taking a step further towards reliable and sustainable engineering solutions, based on more conscious use of the plants' dynamics, we decide to address in this thesis two fundamental challenges related to constrained control and observation. In the first part of this work, we consider the control of uncertain nonlinear systems with input and state constraints, for which a general approach remains elusive. In this context, we propose a novel closed-form solution based on Explicit Reference Governors and Barrier Lyapunov Functions. Notably, it is shown that adaptive strategies can be embedded in the constrained controller design, thus handling parametric uncertainties that often hinder the resulting performance of constraint-aware techniques. The second part of the thesis deals with the global observation of dynamical systems subject to topological constraints, such as those evolving on Lie groups or homogeneous spaces. Here, general observability analysis tools are overviewed, and the problem of sensorless control of permanent magnets electrical machines is presented as a case of study. Through simulation and experimental results, we demonstrate that the proposed formalism leads to high control performance and simple implementation in embedded digital controllers

Lifelong Learning Control of Nonlinear Systems with Constraints using Multilayer Neural Networks with Application to Mobile Robot Tracking

This Paper Presents a Novel Lifelong Multilayer Neural Network (MNN) Tracking Approach for an Uncertain Nonlinear Continuous-Time Strict Feedback System that is Subject to Time-Varying State Constraints. the Proposed Method Uses a Time-Varying Barrier Function to Accommodate the Constraints Leading to the Development of an Efficient Control Scheme. the Unknown Dynamics Are Approximated using a MNN, with Weights Tuned using a Singular Value Decomposition (SVD)-Based Technique. an Online Lifelong Learning (LL) based Elastic Weight Consolidation (EWC) Scheme is Also Incorporated to Alleviate the Issue of Catastrophic Forgetting. the Stability of the overall Closed-Loop System is Analyzed using Lyapunov Analysis. the Effectiveness of the Proposed Method is Demonstrated by using a Quadratic Cost Function through a Numerical Example of Mobile Robot Control Which Demonstrates a 38% Total Cost Reduction When Compared to the Recent Literature and 6% Cost Reduction is Observed When the Proposed Method with LL is Compared to the Proposed Method Without LL

Adaptive Safety-critical Control with Uncertainty Estimation for Human-robot Collaboration

In advanced manufacturing, strict safety guarantees are required to allow humans and robots to work together in a shared workspace. One of the challenges in this application field is the variety and unpredictability of human behavior, leading to potential dangers for human coworkers. This paper presents a novel control framework by adopting safety-critical control and uncertainty estimation for human-robot collaboration. Additionally, to select the shortest path during collaboration, a novel quadratic penalty method is presented. The innovation of the proposed approach is that the proposed controller will prevent the robot from violating any safety constraints even in cases where humans move accidentally in a collaboration task. This is implemented by the combination of a time-varying integral barrier Lyapunov function (TVIBLF) and an adaptive exponential control barrier function (AECBF) to achieve a flexible mode switch between path tracking and collision avoidance with guaranteed closed-loop system stability. The performance of our approach is demonstrated in simulation studies on a 7-DOF robot manipulator. Additionally, a comparison between the tasks involving static and dynamic targets is provided

Adaptive Control of Unknown Pure Feedback Systems with Pure State Constraints

This paper deals with the tracking control problem for a class of unknown pure feedback system with pure state constraints on the state variables and unknown time-varying bounded disturbances. An adaptive controller is presented for such systems for the very first time. The controller is designed using the backstepping method. While designing it, Barrier Lyapunov Functions is used so that the state variables do not contravene its constraints. In order to cope with the unknown dynamics of the system, an online approximator is designed using a neural network with a novel adaptive law for its weight update. In the stability analysis of the system, the time derivative of Lyapunov function involves known virtual control coefficient with unknown direction and to deal with such problem Nussbaum gain is used to design the control law. Furthermore, to make the controller robust and computationally inexpensive, a novel disturbance observer is designed to estimate the disturbance along with neural network approximation error and the time derivative of virtual control input. The effectiveness of the proposed approach is demonstrated through a simulation study on the third-order nonlinear system

Iterative Convex Optimization for Model Predictive Control with Discrete-Time High-Order Control Barrier Functions

Safety is one of the fundamental challenges in control theory. Recently, multi-step optimal control problems for discrete-time dynamical systems were formulated to enforce stability, while subject to input constraints as well as safety-critical requirements using discrete-time control barrier functions within a model predictive control (MPC) framework. Existing work usually focus on the feasibility or the safety for the optimization problem, and the majority of the existing work restrict the discussions to relative-degree one for control barrier function. Additionally, the real-time computation is challenging when a large horizon is considered in the MPC problem for relative-degree one or high-order control barrier functions. In this paper, we propose a framework that solves the safety-critical MPC problem in an iterative optimization, which is applicable for any relative-degree control barrier functions. In the proposed formulation, the nonlinear system dynamics as well as the safety constraints modeled as discrete-time high-order control barrier functions (DHOCBF) are linearized at each time step. Our formulation is generally valid for any control barrier function with an arbitrary relative-degree. The advantages of fast computational performance with safety guarantee are analyzed and validated with numerical results