Unconstrained Control Research Articles

Optimized Backstepping Cooperative Control for Output-Constrained Stochastic Nonlinear Network Systems via a Multibridge-Hole Function.

In this article, a new leader-following tracking control approach is investigated for stochastic multiagent systems with multibridge-hole output constraints. The multibridge-hole output constraints mean that the output of the system is constrained in some intervals and unconstrained in other intervals. The constrained and unconstrained intervals can be set arbitrarily. By designing a new shift function to construct the barrier Lyapunov function, the optimal controller is constructed by combining the backstepping technique with the adaptive dynamic programming technique. The model network is used to estimate the unknown disturbances and uncertainty terms in the system. The critic network and the actor network are constructed such that the designed controller adheres to the Bellman optimality principle and gives the optimal solution of the system. The proposed control method is versatile and compatible with various types of output constrained control problems, such as unconstrained control problems, constrained control problems, and delay constrained problems without changing the structure of the controller. Finally, some simulation results are given to verify the effectiveness of the method.

Cascaded safety trajectory tracking control for a hovercraft with double-loop prescribed performance and state constraints

ABSTRACT This paper presents a cascaded safety trajectory tracking control scheme for hovercraft, addressing dump disturbances with a novel double-loop strategy that enforces prescribed performance and state constraints. Initially, an Adaptive Prescribed-Time Extended State Observer (APESO) is meticulously crafted to estimate lumped disturbances accurately. Subsequent to this, virtual velocity control laws are established through Double Power Appointed-Time Performance Function (DPATPF) combined with an Asymmetric Barrier Lyapunov Function (ABLF), streamlining the position error into a more manageable, equivalent unconstrained control system format. To effectively manage velocity safety constraints, a Unified Barrier Function (UBF) is introduced, ensuring that hovercraft velocities adhere to asymmetric safety boundary. The entire system state is rigorously ultimately uniformly bounded, in strict compliance with cascade control theories and Lyapunov stability criteria. Through simulation, we demonstrate the superior performance and effectiveness of the proposed control strategy, showcasing its potential for enhancing hovercraft navigational safety and reliability.

Reinforcement learning based temperature control of a fermentation bioreactor for ethanol production.

Ethanol production is a significant industrial bioprocess for energy. The primary objective of this study is to control the process reactor temperature to get the desired product, that is, ethanol. Advanced model-based control systems face challenges due to model-process mismatch, but Reinforcement Learning (RL) is a class of machine learning which can help by allowing agents to learn policies directly from the environment. Hence a RL algorithm called twin delayed deep deterministic policy gradient (TD3) is employed. The control of reactor temperature is categorized into two categories namely unconstrained and constrained control approaches. The TD3 with various reward functions are tested on a nonlinear bioreactor model. The results are compared with existing popular RL algorithm, namely, deep deterministic policy gradient (DDPG) algorithm with a performance measure such as mean squared error (MSE). In the unconstrained control of the bioreactor, the TD3 based controller designed with the integral absolute error (IAE) reward yields a lower MSE of 0.22, whereas the DDPG produces an MSE of 0.29. Similarly, in the case of constrained controller, TD3 based controller designed with the IAE reward yields a lower MSE of 0.38, whereas DDPG produces an MSE of 0.48. In addition, the TD3 trained agent successfully rejects the disturbances, namely, input flow rate and inlet temperature in addition to a setpoint change with better performance metrics.

A constrained control framework for unmanned aerial vehicles based on Explicit Reference Governor

This paper tackles the constrained control problem of unmanned aerial vehicles with planar multirotors. The proposed solution splits the constrained control problem into two separate tasks, i.e. stabilization and constraint enforcement. It is shown that the problems addressed by each individual layer is much simpler than the original combined problem. For the unconstrained control of UAVs we consider a control scheme based on a cascade structure. The Lyapunov function for the stabilized cascaded system is then derived. Using this Lyapunov function, we develop an Explicit Reference Governor for constraint enforcement. Numerical simulation shows the effectiveness of the proposed approach.

Design and analysis of ELM-based predefined time sliding mode adaptive controller for PMLM position control under physical constraints

Achieving accurate position tracking for robotics and industrial servo systems is an extremely challenging task, particularly when dealing with control saturation, parameter perturbation, and external disturbance. To address these challenges, a predefined time convergent sliding mode adaptive controller (PTCSMAC) has been proposed for a permanent magnet linear motor (PMLM). A novel sliding mode surface (SMS) with predefined time convergence PDTC has been constructed, which ensures that the error converges to zero within the prescribed time. The system not only meets the expected performance standards but also has a uniformly bounded motor speed. The trajectory tracking error in SMS is proven to converge to zero within the predefined time. This predefined time stability of the closed-loop system has been demonstrated by using the Lyapunov stability criterion with PDTC. The convergence time (CT) can be arbitrarily set, and the upper bound of it is not affected by the initial value and control parameters of the system. A new updated version of extreme learning machine (ELM) is introduced to approximate the uncertain part of the system based on PDTC. The ELM is also provided with the hyperbolic tangent function to estimate the saturation constraint. This is done by converting the function into a linear function concerning the unconstrained control input variable. Then, based on established stability, a novel sliding mode adaptive controller (PTCSMAC) with predefined time convergence is designed. The convergence time (CT) of the controller is unaffected by the initial conditions as well as the control parameters. The rigorous numerical simulations on the PMLM model with complex disturbances verify the strong robustness and high-precision tracking characteristic of the proposed control law.

A Barrier-Function-Based Second-Order Sliding Mode Control With Optimal Reaching for Full-State and Input-Constrained Nonlinear Systems

This paper considers the design of a minimum-time Second Order Sliding Mode Control (SOSMC) method for a class of full state and input constrained nonlinear systems. In this study, to enable the handling of the state and input constraints, a barrier function-based state transformation method is employed to convert the original control problem to an unconstrained control problem. Using the new representation of the system dynamics and the input-state linearization technique, a novel sliding manifold is proposed. Relying on the proposed sliding manifold on the concept of the Robust Fuller's Problem, a second order sliding mode controller is developed to achieve optimal reaching time in the presence of the considered constraints. Furthermore, as a tool for computing the reaching time of the proposed minimum-time SOSMC, a new computational method is developed. To quantify the effects of the constraints on the optimal reaching time, the reaching time of the proposed SOSMC and the unconstrained minimum-time SOSMC methods are compared. Numerical simulations verify the efficacy of the proposed control method making reference, as an illustrative example, to the Duffing oscillator.

Control Lyapunov–Barrier function based model predictive control for stochastic nonlinear affine systems

AbstractA stochastic model predictive control (MPC) framework is presented in this paper for nonlinear affine systems with stability and feasibility guarantee. We first introduce the concept of stochastic control Lyapunov–Barrier function (CLBF) and provide a method to construct CLBF by combining an unconstrained control Lyapunov function (CLF) and control barrier functions. The unconstrained CLF is obtained from its corresponding semi‐linear system through dynamic feedback linearization. Based on the constructed CLBF, we utilize sampled‐data MPC framework to deal with states and inputs constraints, and to analyze stability of closed‐loop systems. Moreover, event‐triggering mechanisms are integrated into MPC framework to improve performance during sampling intervals. The proposed CLBF based stochastic MPC is validated via an obstacle avoidance example.

Generalized efficient robust predictive control for networked interval type-2 T–S fuzzy system with adaptive event-triggered scheme

This article studies the generalized efficient robust predictive control (GERPC) for the nonlinear systems denoted by interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy model over networks with consideration of packet dropout, bounded disturbance and adaptive event-triggered scheme (AETS). First, the packet dropout is described by a Bernoulli process, and an AETS with thresholds that can be self-regulated according to different situations is employed to decide whether to release data into the communication network, so as to reduce the data transmission frequency and the network burden; Second, taking into consideration of packet dropout and AETS, a unified IT2 T–S fuzzy control model based on GERPC is established, and the stability of closed-loop system with bounded disturbance is guaranteed by quadratic boundedness (QB) technique; Third, generalized efficient robust predictive controller is designed to obtain a larger initial feasible region, smaller online computation and acceptable control performance. The unconstrained control law is designed offline, and a new variable will be optimized online to achieve good control performance, which is introduced to adjust the control quantity. Then, the convex LMI reformulation method is utilized to handle non-convex terms in optimization problem, and the effectiveness of the GERPC algorithm is proved by the matrix partition technique. At last, the effectiveness of the designed controller based on the GERPC strategy is verified by a given simulation experiment.

Constrained control using novel nonlinear mapping for underactuated unmanned surface vehicles with unknown sideslip angle

This paper addresses the problem of guidance and control for underactuated unmanned surface vehicles (USVs) with state constraints and input saturation, in support of enabling an underactuated USV to follow a parameterized curved path in the case of unknown sideslip angle and cross-tracking error constraint. First, a cross-tracking error constraint line-of-sight (LOS) guidance law with sideslip angle compensation is originally designed to guide an underactuated USV to convergence to the desired path within a time-varying cross-tracking error constraint. Second, a novel nonlinear mapping (NM) function is first constructed to map the heading and surge control subsystems with state constraints to unconstrained nonlinear systems, transforming the constrained control problem into the unconstrained control problem. Subsequently, adaptive fuzzy control laws are designed to achieve the control objectives for the USV using the new unconstrained nonlinear systems with unknown disturbance and input saturation. Then, a series of theoretical analyses using input-to-state stability theories are presented to prove the boundness of the tracking errors for the underactuated USV during path following. Finally, numerical results obtained using a physics-based simulation model are shown to reveal the effectiveness of the guidance and control algorithms.

Formation Control for Leader–Follower Wheeled Mobile Robots Based on Embedded Control Technique

The formation control problem for leader–follower wheeled mobile robots (WMRs) is investigated in this article. A formation control strategy is proposed based on the embedded control technique. Different from the conventional design philosophy of designing the formation controller based on the formation tracking errors directly, the proposed strategy decomposes the formation control task into two subtasks. One is the virtual signal generator (i.e., virtual follower) design, and the other is the trajectory tracking controller design. The virtual signal generator is devised to act as a virtual follower such that it “achieves” the desired formation control goal, whose output is taken as the reference trajectory for the follower. To solve the subtask of trajectory tracking controller design, an unconstrained controller and a constrained controller with saturated velocities are designed, respectively. A rigorous stability analysis of the closed-loop system is given under these two kinds of controllers. Comparative simulations and experiments among the unconstrained controller with higher gains/lower gains and the constrained controller are given to illustrate the feasibility and effectiveness of the proposed formation control strategy.

A sufficient condition for optimal control problem of fully coupled forward‐backward stochastic systems with jumps: A state‐constrained control approach

AbstractWe study the stochastic optimal control problem for fully coupled forward‐backward stochastic differential equations (FBSDEs) with jump diffusions. A major technical challenge of such problems arises from the dependence of the (forward) diffusion term on the backward SDE and the presence of jump diffusions. Previously, this class of problems has been solved via only the stochastic maximum principle, which guarantees only the necessary condition of optimality and requires identifying unknown parameters in the corresponding variational inequality. Our paper provides an alternative approach, which constitutes the sufficient condition for optimality. Specifically, the original fully coupled FBSDE control problem (referred to as (P)) is converted into the terminal state‐constrained forward stochastic control problem (referred to as ) that includes additional (possibly unbounded) control variables. Then is solved via the backward reachability analysis, by which the value function of is expressed as the zero‐level set of the value function for the auxiliary unconstrained (forward) control problem (referred to as ). Unlike ), is an unconstrained problem, which includes additional control variables as a consequence of the martingale representation theorem. We show that the value function for is the unique viscosity solution to the associated integro‐type Hamilton‐Jacobi‐Bellman (HJB) equation. The viscosity solution analysis presented in our paper requires a new technique due to additional control variables in the Hamiltonian maximization and the presence of the nonlocal integral operator in terms of the (singular) Lévy measure. To solve the original problem (P), we reverse our approach. Specifically, we first solve to obtain the value function using the verification theorem and the viscosity solution of the HJB equation. Then is solved by characterizing the zero‐level set of the value function of , from which the optimal solution of (P) can be constructed. To illustrate the theoretical results of this paper, applications to the linear‐quadratic problem for fully coupled FBSDEs with jumps are also presented.

Adaptive neural network–based trajectory tracking non-affine control of hovercraft with double-loop constraint performance

This study investigates the design of a trajectory tracking constraint control method for hovercraft non-affine formulations via neural network approximation. The tracking scheme comprises an outer closed-loop of attitude and an inner closed-loop of velocity (double-loop). First, a performance function is devised to constrain the attitude errors and then a transformed error function is introduced to simplify it into an equivalent unconstrained control system. Next, an improved asymmetric integral barrier Lyapunov function is designed to address asymmetric velocity constraint problems, which can guarantee the safe turning motion or performance required at high speed. Furthermore, neural networks are employed to estimate the unknown terms of each subsystem, which solve system uncertainties and non-affine dynamics problems. The double closed-loop control system is ultimately uniformly bounded by utilizing the Lyapunov stability principle. Finally, simulation results are presented to verify the tracking performance and effectiveness of the proposed control strategy.

Geometrically Constrained Trajectory Optimization for Multicopters

In this article, we present an optimization-based framework for multicopter trajectory planning subject to geometrical configuration constraints and user-defined dynamic constraints. The basis of the framework is a novel trajectory representation built upon our novel optimality conditions for unconstrained control effort minimization. We design linear-complexity operations on this representation to conduct spatial–temporal deformation under various planning requirements. Smooth maps are utilized to exactly eliminate geometrical constraints in a lightweight fashion. A variety of state-input constraints are supported by the decoupling of dense constraint evaluation from sparse parameterization and the backward differentiation of flatness map. As a result, this framework transforms a generally constrained multicopter planning problem into an unconstrained optimization that can be solved reliably and efficiently. Our framework bridges the gaps among solution quality, planning efficiency, and constraint fidelity for a multicopter with limited resources and maneuvering capability. Its generality and robustness are both demonstrated by applications to different flight tasks. Extensive simulations and benchmarks are also conducted to show its capability of generating high-quality solutions while retaining the computation speed against other specialized methods by orders of magnitude.

Stochastic optimal control of pre-exposure prophylaxis for HIV infection

The aim of the paper is to apply the stochastic optimal control problem in order to optimize the number of individual which will have the pre-exposure prophylaxis (PReP) treatment in the stochastic model for HIV/AIDS with PReP. By using the stochastic maximum principle, we derive the stochastic optimal control of PReP for the unconstrained control problem. Furthermore, by combining the stochastic maximum principle with a version of the Lagrange multiplier method, we solve the PReP problem for two different types of budget constrains with a given constrain for the costs (possible of different kind, transportation, price of the treatment, etc.). Obtained results for the different percentage of the individuals who got the vaccine, as well as results for unconstrained and constrained problems, are illustrated by a numerical example.

Control of Dynamic Positioning System with Disturbance Observer for Autonomous Marine Surface Vessels.

The main goal of the research is to design an efficient controller for a dynamic positioning system for autonomous surface ships using the backstepping technique for the case of full-state feedback in the presence of unknown external disturbances. The obtained control commands are distributed to each actuator of the overactuated vessel via unconstrained control allocation. The numerical hydrodynamic model of CyberShip I and the model of environmental disturbances are applied to simulate the operation of the ship control system using the time domain analysis. Simulation studies are presented to illustrate the effectiveness of the proposed controller and its robustness to external disturbances.

Revisiting a fixed-point hierarchical control design for cryogenic refrigerators under constraints, nonlinearities and real-time considerations

This paper presents an extension of a recently proposed hierarchical control framework applied to linearization-based unconstrained control of a cryogenic refrigerator. The extension concerns the validation of the framework in the presence of both nonlinear models and constraints. It is also shown that real-time handling of these features requires a specific complexity reduction technique. This technique performs the distribution of the optimization process over cyclically changed decision variables aiming at limiting the number of iterations per updating period. Numerical simulations are proposed in order to show the impact of the parameters choices and to assess the real-time implementability of the proposed framework.

Tube-model predictive control based on sum of squares for hypersonic vehicle with state-dependent input constraints

In this paper, tube-model predictive control based on the sum of squares technique is developed for hypersonic vehicles with state-dependent input constraints. Firstly, the longitudinal non-linear model in the presence of uncertain parameters is transformed into the polytopic linear parameter varying model with bounded disturbance by feedback linearization. Then the actual input constraints are converted to the virtual state-dependent input constraints in linear multivariable polynomial. A composite feedback control law based on tube-model predictive control is designed into a convex combination of unconstrained and constrained control. The real control law can be obtained by inversion. The sum of squares technique is used to transform the polynomial constraints into the convex matrix sum of squares condition via linear matrix inequality. Finally, simulation results verify the effectiveness of the proposed controller.

Robust model predictive control for hypersonic vehicle with state‐dependent input constraints and parameter uncertainty

AbstractIn this article, a robust model predictive control strategy based on sum‐of‐squares (SOS‐RMPC) is proposed for hypersonic vehicle with state‐dependent input constraints and uncertain parameters. Based on feedback linearization model of hypersonic vehicle, the polytopic linear parameter varying error model with bounded disturbance is established for reference trajectory tracking. The real limits of the actual control inputs are transformed into the constraints of the virtual inputs equivalently with the state‐dependent nonlinear functions. Further, the multivariate linear fitting is used to approximate the state‐dependent input constraints into polynomials. A weighted composite virtual control is formulated as the combination of unconstrained control and auxiliary control. SOS technique is introduced to cast the polynomial constraints into the convex matrix SOS conditions via linear matrix inequality. The virtual control law can be obtained by solving a SOS‐RMPC convex optimization with infinite horizon. The invariant set is designed for the undisturbed error states and the norm‐bounding theory is applied to ensure that the predictive error states with disturbance can remain in the same invariant set. The real control law is obtained by inverse control. The simulation verifies the performance of the designed controller.

Adaptive cross backstepping control for a class of nonstrict feedback nonlinear systems with partial state constraints

AbstractThe tracking control problem for a class of partial state constrained nonlinear system is studied in this article. The system is divided into two semistrict feedback nonlinear subsystems, one is state constrained and the other is state free. By means of state transformation, the state constraint problem is transformed into the bounded problem of the transformed function. Compared with the barrier Lyapunov function (BLF) method, it not only solves the state constraint problem but also circumvents the feasibility check on virtual controllers. Based on the cross backstepping control, the constrained controller and unconstrained controller are designed simultaneously. It solves the coupling problem effectively in the design of cross processing control. On the other hand, dynamic surface control is used which effectively avoids “computation explosion” caused by backstepping control. The designed controllers can ensure the error signals converge to a small neighbourhood of zero and keep the asymmetric time‐varying constraints on system partial states are satisfied for all the time. Finally, simulation experiments are carried out on a hyperchaotic Rössler system to verify the efficacy of the control scheme.

Motor and Perception Constrained NMPC for Torque-Controlled Generic Aerial Vehicles

This letter presents a perception-aware and motor-level non-linear model predictive control scheme for multi-rotor aerial vehicles. Our formulation considers both real actuation limitations of the platform, and realistic perception objectives for the visibility coverage of an environmental feature while performing a reference task. It directly produces the rotor-level (torque) inputs of the platform motors at high frequency, hence it does not require an intermediate unconstrained controller to work. It is also meant to be generic, by covering standard coplanar quadrotors as well as tilted-propeller multi-rotors. We propose an open-source fully onboard implementation of the method, capable of running at 500 Hz under the intermittent and noisy measurements of one or more cameras. The implementation is extensively tested both in simulation and in real experiments with two substantially different multi-rotor platforms, an underactuated and a fully actuated one, both equipped with two cameras, clearly demonstrating the practicability and high performance of the method.