Nonlinear Control Synthesis Research Articles

Immersion and Invariance-Based Nonlinear Control Synthesis for Depth Position of an AUV: Tracking and Regulation

Immersion and Invariance-Based Nonlinear Control Synthesis for Depth Position of an AUV: Tracking and Regulation

Nonlinear Optimal Control for Stochastic Dynamical Systems

This paper presents a comprehensive framework addressing optimal nonlinear analysis and feedback control synthesis for nonlinear stochastic dynamical systems. The focus lies on establishing connections between stochastic Lyapunov theory and stochastic Hamilton–Jacobi–Bellman theory within a unified perspective. We demonstrate that the closed-loop nonlinear system’s asymptotic stability in probability is ensured through a Lyapunov function, identified as the solution to the steady-state form of the stochastic Hamilton–Jacobi–Bellman equation. This dual assurance guarantees both stochastic stability and optimality. Additionally, optimal feedback controllers for affine nonlinear systems are developed using an inverse optimality framework tailored to the stochastic stabilization problem. Furthermore, the paper derives stability margins for optimal and inverse optimal stochastic feedback regulators. Gain, sector, and disk margin guarantees are established for nonlinear stochastic dynamical systems controlled by nonlinear optimal and inverse optimal Hamilton–Jacobi–Bellman controllers.

Pursuer Coordination Against a Fast Evader via Coverage Control

Scalable pursuer coordination for reach-avoid games against a fast evader are developed leveraging coverage control over manifolds. The maintenance of a manifold, termed defense surface, prevents the evader and its target from occupying the same half-space and shown sufficient as a cooperative capture strategy. Nonlinear control synthesis continually reconfigures the pursuers to enable a defense surface via coverage. Simulation results empirically validate that the proposed condition serves as a surrogate objective for pursuer team coordination.

Nonlinear Controller Synthesis for HIV Dynamics Based on SOS

Nonlinear Controller Synthesis for HIV Dynamics Based on SOS

Multicriteria Parametric Optimization of Nonlinear Robust Control with Two Degrees of Freedom by a Discrete-Continuous Plant

A multicriteria parametric optimization of nonlinear robust control with two degrees of freedom by a discrete-continuous plant has been developed to increase accuracy and reduce sensitivity to uncertain plant parameters. Such plants are mounted on a moving base, on which sensors for angles, angular velocities and angular accelerations are installed. To increase the accuracy of control, systems with two degrees of freedom, which include control with feedback and a closed-loop, and with direct connections and open-loop control of the setting and disturbing effects, are used. The multicriteria optimization of nonlinear robust control with two degrees of freedom by a discrete-continuous plant is reduced to the solution of the Hamilton-Jacobi-Isaacs equations. The robust control target vector is calculated as a solution of a zero-sum antagonistic vector game. The vector payoffs of this game are direct indexes performance vector presented in the system in different modes of its operation. The calculation of the vector payoffs of this game is related to the simulation of the synthesized nonlinear system for different operating modes of the system, input signals and values of the plant parameters. The solutions of this vector game are calculated on the basis of the system of Pareto-optimal solutions, taking into account the binary relations of preferences, on the basis of the stochastic metaheuristic of Archimedes optimization algorithm by several swarms. Thanks to the synthesis of nonlinear robust control with two degrees of freedom by a discrete-continuous object, it is shown that the use of synthesized controllers made it possible to increase the accuracy of control of an electromechanical system with distributed parameters of the mechanical part to reduce the time of transient processes by 1.5–2 times, reduce dispersion of errors by 1.3 times and reduce the sensitivity of the system to changes in the plant parameters in comparison with typical controllers used in existing systems. Further improvement of control accuracy is restrained by energy limitations of executive mechanisms and information limitations of measuring devices.

Nonlinear dynamic analysis and control synthesis for the Swinging Omnidirectional (SWINGO) Wave Energy Converter

We introduce, in this paper, an analysis of the dynamics of the Swinging Omnidirectional (SWINGO) wave energy converter. Such a device is an inertial reacting Wave Energy Converter (WEC), that exploits the dynamics of a gyropendulum mechanism which, being excited by the wave-induced whirling motion (i.e. coupling between pitch and roll on a floater), can successively activate an electric generator connected to the grid. In particular, we apply the harmonic balance method, tuned to the system fundamental harmonic, to identify the effect of nonlinearities on the SWINGO dynamics and their impact on energy production. Furthermore, we present the so-called van der Pol plane to assess the stability properties of the system. The SWINGO model is derived via a Lagrangian approach formulated with respect to quasi-coordinates. We demonstrate that multi-stability behaviour can be found for this nonlinear system, completely absent in its associated linearisation. Finally, we synthesise so-called ‘passive’ (i.e. proportional) energy-maximising controllers by leveraging the Harmonic Balance (HB) procedure, providing control parameters which are effectively tuned by exploiting the presented nonlinear description of SWINGO.

Fractional Order Modeling of PWR Pressurizer Dynamics and Fractional Order Nonlinear H∞ Controllers Design in LabVIEW

The novel fractional order intelligent transient dynamics and advanced fractional order nonlinear robust control synthesis scheme of the Pressurized Water Reactor (PWR) pressurizer are addressed in this research work. The Graphical User Interface (GUI) is designed for closed-loop model-based PWR pressurizer dynamical studies in LabVIEW. Based on the demand for power, the reactor power and turbine power are predicted using a fractional order backpropagation algorithm in an open loop configuration. Using turbine power and heater power as input variables, pressurizer level, pressurizer pressure and coolant average temperature as output variables, the open loop multi-input multi-output (MIMO) dynamic model of pressurizer is estimated using fractional order artificial intelligence in LabVIEW. Four fractional order robust nonlinear H∞ sub-controllers are designed for charging flow, spray flow, proportional heaters power and backup heaters power. All the dynamic controller models are in fractional order nonlinear H∞ framework and are designed in LabVIEW. The performance of the proposed design work is evaluated in closed loop configuration at 100 %, 75 % and 15 % in steady state conditions. Dynamic transient analysis is performed from 100% to 90% power reduction scenario and found satisfactory and within design limits and robust bounds.

The method of multi objective synthesis of nonlinear robust control by multimass electromechanical systems

Aim. Development of the method of multi objective synthesis of nonlinear robust control by multimass electromechanical systems to satisfy various requirements for the operation of multi-mass systems in various modes. Methodology. The problem of multi objective synthesis of nonlinear robust control of multimass electromechanical systems is formulated and the possibility of satisfying various requirements for the operation of such systems in various modes based on the concept of functionally multiple membership of the state vector and the solution of the Hamilton-Jacobi-Isaacs equation is shown. A method for choosing weight matrices with the help the vector of purpose of nonlinear robust control is formed by solving a zero-sum vector antagonistic game has been substantiated and developed. Results. The results multi objective synthesis of nonlinear robust two-mass electromechanical servo systems in which differences requirements for the operation of such systems in various modes were satisfied are given. Based on the results of modeling and experimental studies it is established, that with the help of synthesized robust nonlinear controllers, it is possible to improve of quality indicators of two-mass electromechanical servo system in comparison with the system with standard regulators. Originality. For the first time the method of multi objective synthesis of nonlinear robust control by multimass electromechanical systems to satisfy various requirements for the operation of multimass systems in various modes is developed. Practical value. From the point of view of the practical implementation the possibility of solving the problem of multi objective synthesis of nonlinear robust control systems to satisfy various requirements for the operation of multimass electromechanical systems in various modes is shown.

Active management strategy for supply chain system using nonlinear control synthesis.

Nonlinear dynamical behaviours with chaotic phenomena are commonly observed in a typical logistics model and supply chain system. Bullwhip effect has been widely recognized as one of the main issues on affecting the supply chain management. In essence, this phenomenon will lead to unnecessary consumption and waste of natural and social resources by demand variability amplification as moving up in the supply chain networks. However, traditional modelling approaches may become complicated in dealing with uncertainty and chaotic behaviour that are prevalent in real supply chains. System dynamics theory has been employed as a potentially effective strategy to cope with chaotic supply chains which are unpredictable behaviours in time. Four-dimensional differential equations which exhibit chaotic behaviours are constructed to describe a multi-echelon supply chain with bullwhip effect. Furthermore, modern control theory is applied to deal with the multi-stage supply chain optimization problems against disruptions. Specifically, the novel fractional order adaptive sliding mode control (FO-ASMC) algorithm has been implemented for ensuring efficient supply chain management. In addition, the chaos synchronization scheme is implemented in an attempt to regulate the supply chain systems under the impact of extensive uncertainties caused by tumultuous real market. It is found that the chaos synchronization is effectively realised by new FO-ASMC theory to manage advanced supply chain networks. Finally, this advanced management optimization offers a new class of intelligent applications that connects demand to supply and planning to execution across the entire supply chains.

Robust nonlinear control synthesis by using centre manifold-based reduced models for the mitigating of friction-induced vibration

Robust nonlinear control synthesis by using centre manifold-based reduced models for the mitigating of friction-induced vibration

A Convex Data-Driven Approach for Nonlinear Control Synthesis

We consider a class of nonlinear control synthesis problems where the underlying mathematical models are not explicitly known. We propose a data-driven approach to stabilize the systems when only sample trajectories of the dynamics are accessible. Our method is built on the density-function-based stability certificate that is the dual to the Lyapunov function for dynamic systems. Unlike Lyapunov-based methods, density functions lead to a convex formulation for a joint search of the control strategy and the stability certificate. This type of convex problem can be solved efficiently using the machinery of the sum of squares (SOS). For the data-driven part, we exploit the fact that the duality results in the stability theory can be understood through the lens of Perron–Frobenius and Koopman operators. This allows us to use data-driven methods to approximate these operators and combine them with the SOS techniques to establish a convex formulation of control synthesis. The efficacy of the proposed approach is demonstrated through several examples.

Container throughput analysis and seaport operations management using nonlinear control synthesis

This paper is to explore the dynamical analysis and active control synthesis for improving seaport operations through system optimization. First, the multi-dimensional system of the fractional Lotka-Volterra model is utilized to investigate its underlying dynamics of port competition and cooperation for container throughput. The nonlinear dynamical behaviors are intensely examined by using eigenvalue evaluation, bifurcation analysis and time series analysis to illustrate the stability of the competition and collaboration model. With the system theory based on fractional order calculus, various dynamic properties of ports system have been discovered. Based on the dynamical analysis, adaptive fractional-order sliding mode control with artificial neural network algorithm has been realized for port growth rate improvement against disruptions. Furthermore, the proposed approach is successfully validated by the case study of major Korean seaports for improving port operations through neural network prediction. The decision making policies implemented by control algorithms are guaranteed to improve the port growth rate against disruptions. Specifically, the novel management strategy is to provide managerial insights and innovative solutions for seaport authorities who can make more efficient strategic planning for handling risk management in maritime logistics.

A Robust Nonlinear Model Reference Adaptive Control for Disturbed Linear Systems: An LMI Approach

In this article, a robust nonlinear model reference adaptive control (MRAC) is proposed for disturbed linear systems, i.e., linear systems with parameter uncertainties, and external time-dependent perturbations or nonlinear unmodeled dynamics matched with the control input. The proposed nonlinear control law is composed of two nonlinear adaptive gains. Such adaptive gains allow the control to counteract the effects of some perturbations and nonlinear unmodeled dynamics ensuring asymptotic convergence of the tracking error to zero, and the boundedness of the adaptive gains. The nonlinear controller synthesis is given by a constructive method based on the solution of linear matrix inequalities. Besides, the simulation results show that, due to the nonlinearities, the rate of convergence of the proposed algorithm is faster than that provided by a classic MRAC.

Synthesis of non-linear controller to energy efficiency for damped-elastic-jointed inverted pendulum

In the paper we propose a synthetic way of the nonlinear controller for the damped-elastic-jointed inverted pendulum. The controller is designed based on the synergistic approach, the global variables are built on the asymptotically stable manifolds and the fast acting objective function is energy efficient. The effectiveness of the export method is proven through simulation results and compared with other methods.

Handling Torque Input Constraints Under Robust Nonlinear Regulation Control of Robotic Systems with Parametric Uncertainties

This paper proposes a methodology of handling torque input constraints under robust nonlinear regulation control synthesis for robotic systems with parametric uncertainties. The proposed method is composed of: (i) an inner loop controller design applying a nonlinear geometric control via feedback linearization to transform uncertain robotic systems into worst-case uncertain linear system, (ii) a new method of torque input constraint mapping the constraints on the input torques into a constraint on new control inputs of the uncertain linear system through the feedback linearizing control law, and (iii) a new approach of outer loop controller design using robust H( static state feedback controller to handle the remaining uncertain nonlinear parts and to satisfy the mapped input constraints. In order to verify the correctness and the performance of the proposed method, it is demonstrated via simulation of position control problem for a two-link robotic system.

Sum-of-Squares Flight Control Synthesis for Deep-Stall Recovery

Certification of inflight loss-of-control recovery is complicated by the highly nonlinear flight dynamics beyond stall. In lieu of extensive Monte Carlo simulations for flight control certification, sum-of-squares programming techniques provide an algebraic approach to the problem of nonlinear control synthesis and analysis. However, reliance on polynomial models has hitherto limited applicability to aeronautical control problems. Taking advantage of recently proposed piecewise polynomial models, this paper revisits sum-of-squares techniques for recovery of an aircraft from deep-stall conditions using a realistic yet tractable aerodynamic model. The local stability analysis of classical controllers is presented as well as synthesis of polynomial feedback laws with the objective of enlarging their nonlinear region of attraction. A newly developed synthesis algorithm for infinite-horizon backward reachability facilitates the design of recovery control laws, ensuring stable recovery by design. The paper’s results motivate future research in aeronautical sum-of-squares applications.

Underactuated Coupled Nonlinear Adaptive Control Synthesis Using U-Model for Multivariable Unmanned Marine Robotics

This paper presents the control modelling and synthesis using a coupled multivariable under-actuated nonlinear adaptive U-model approach for an unmanned marine robotic platform. A nonlinear marine robotics model based on the dynamic equation using the Newtonian method and derivation with respect to the kinematics equations and rigid-body mass matrixes are explained. This nonlinear marine robotics model represents the underwater thruster dynamics, marine robotics dynamics and kinematics related to the earth-fixed frame. Coupled multivariable nonlinear adaptive control synthesis using a U-model approach for the Remotely Operated Vehicle (ROV) and Unmanned Surface Vessel (USV) represent an unmanned marine robotics application. A comparison is presented for the proposed nonlinear control approach between the U-model control approach with nonlinear Fuzzy Logic Control and Sliding Mode Control for the ROV and USV platforms. The results show minimum mean square error values and tracking performance between the plant or system model with the proposed method. Lastly, robustness and stability analysis for the proposed U-Model nonlinear control approach are presented by implementing an adaptive learning rate value.

Approximated Constrained Optimal Control subject to Variable Parameters

Implementing optimal controllers on embedded systems can be challenging as it requires the solution of an optimization problem in real-time. Furthermore, the a priory verification of stability, e.g. not relying on the possibly numerical solution of an optimization problem is often not possible. We propose a non-linear control synthesis based on an approximated explicit solution of a constrained optimal control problem, which can be efficiently implemented and verified. The control law is derived based on a series expansion of an infinite horizon optimal control problem via Al’brekht‘s Method. In comparison to existing approaches we consider parametric uncertainties. The proposed method provides under certain conditions an approximated solution of the Hamilton–Jacobi–Bellman (HJB) equation. The feedback control law uses a finite number of terms of the series expansion, and therefore the evaluation does not require intensive online computation. Furthermore, the optimal control strategy does not only achieve an approximated infinite horizon performance but is also parameterized in terms of the varying parameters which are assumed to be known. We provide a proof of convergence and existence of the optimal control law. Simulation results with a non-linear quadcopter example show the effectiveness of the proposed strategy.

Nonlinear robust control of high-speed supercavitating vehicle in the vertical plane

The supercavitating vehicle can quickly become unstable under the influence of the planing force and external disturbances due to waves and currents. The planing force demonstrates nonlinear characteristics which can be described by the vehicle state variables. Strict standards for maneuvering strategy are required for high-speed vehicles to operate, particularly guidance, navigation, and control of underwater maneuver. In reality, the high-speed supercavitating vehicle dynamics present various control issues and challenges. This article proposes the nonlinear robust control synthesis to manipulate the vertical plane of the high-speed supercavitating vehicle against the planing force or parameter variations as well as external disturbances. The control synthesis is implemented by solving an algebraic Riccati equation at each iteration of the control algorithm with the updated system states, which is a so-called state-dependent Riccati equation. The control loops in the dive-plane satisfy an [Formula: see text] performance criterion that can reject external disturbances with perturbations. Simulation results show that the controlled vehicle system guarantees fast transient responses with steady-state performance. Besides, the proposed controller can eliminate up to 62% of disturbances and provides the robust performance against large planing force and parametric uncertainties. This new vehicle technology with active controller offers the potential strategy of higher speed and higher maneuverability solutions for various purposes of underwater maneuvering.

IMPROVING OF ELECTROMECHANICAL STABILIZATION SYSTEMS ACCURACY

Aim. Improving of accuracy parameters and reducing of sensitivity to changes of plant parameters for nonlinear robust tank main armament guidance and stabilization electromechanical systems based on synchronous motor with permanent magnets and vector control. Methodology. The method of multiobjective synthesis of nonlinear robust control by nonlinear tank main armament stabilization electromechanical system taking into account the elastic oscillations of the tank gun barrel as a discrete-continuous plant and with parametric uncertainty based on the multiobjective optimization. The target vector of robust control choice by solving the corresponding multicriterion nonlinear programming problem in which the calculation of the vectors of the objective function and constraints is algorithmic and associated with synthesis of nonlinear robust controllers and modeling of the synthesized system for various modes of operation of the system, with different input signals and for various values of the plant parameters. Synthesis of nonlinear robust controllers and non-linear robust observers reduces to solving the system of Hamilton-Jacobi-Isaacs equations. Results. The results of the synthesis of a nonlinear robust tank main armament guidance and stabilization electromechanical systems are presented. Comparison of the dynamic characteristics of the synthesized tank main armament stabilization electromechanical systems showed that the use of synthesized nonlinear robust controllers allowed to improve the accuracy parameters and reduce the sensitivity of the system to changes of plant parameters in comparison with the existing system. Originality. For the first time carried out the multiobjective synthesis of nonlinear robust tank main armament stabilization electromechanical systems. Practical value. Practical recommendations are given on reasonable choice of the gain matrix for the nonlinear feedbacks of the regulator and the nonlinear observer of the tank main armament stabilization electromechanical systems, which allows improving the dynamic characteristics and reducing the sensitivity of the system to plant parameters changing in comparison with the existing system.