State-dependent Uncertainties Research Articles

Integrated Adaptive Control and Reference Governors for Constrained Systems With State-Dependent Uncertainties

Integrated Adaptive Control and Reference Governors for Constrained Systems With State-Dependent Uncertainties

Semi-global robust stabilisation of disturbed nonlinear systems with state-dependent uncertainties: a DOBC approach

The robust stabilisation for a general class of disturbed nonlinear systems subject to state-dependent uncertainties is addressed in this paper. Different from most existing results, the lumped uncertainty, including external disturbances and model uncertainties, is relaxed to be bounded by some nonlinear functions rather than constants in this paper. Based upon the classical design procedure of disturbance observer-based control (DOBC), a new continuous saturation-based dynamic controller is proposed to estimate the lumped uncertainty. By the delicate design of several compact sets, the qualitative robust stability of the closed-loop system is guaranteed in the sense that all the signals of the closed-loop system can converge to an arbitrarily small compact set in a finite time. Furthermore, when the external disturbances are constants, the semi-global asymptotic stability can also be guaranteed by the proposed controller. Finally, the relationship between system uncertainties and observer gain is shown by a numerical simulation example.

Tracking control for a position-dependent periodic signal in a variable-speed rotational system

This paper concerns the problem of tracking a position-related periodic signal for an uncertain nonlinear rotational system. Applying the additive-state-decomposition (ASD) technique decomposes the original uncertain nonlinear system into two subsystems: A primary linear time-invariant system that performs spatial repetitive control, and a secondary nonlinear system that ensures robust stability of the whole system with respect to unknown nonlinear dynamics and exogenous disturbances. This method has four features: (i) The ASD technique provides an effective way to deal with the coupling between the spatial periodicity and other factors (temporal and state-dependent uncertainties and disturbances) in a rotational system. This technique ensures satisfactory tracking and disturbance rejection performance; (ii) A real-time digital implementation of a spatial repetitive controller enables repetitive control with an exact period in the position. This ensures the synchronous execution of repetitive control in the position domain and robust stability in the time domain; (iii) The method of accurate phase compensation in a spatial repetitive controller leads to a significant improvement in steady-state tracking performance; and (iv) An extended-state observer precisely estimates the overall effect of disturbances. Integrating a disturbance estimate into a control input effectively compensates for disturbances. Stability criteria and design algorithms are presented in detail. Finally, experiments of a rotational speed-control system demonstrate the effectiveness of this method.

Adaptive Sliding-Mode Disturbance Observer-Based Finite-Time Control for Unmanned Aerial Manipulator With Prescribed Performance.

In this article, an adaptive sliding-mode disturbance observer (ASMDO)-based finite-time control scheme with prescribed performance is proposed for an unmanned aerial manipulator (UAM) under uncertainties and external disturbances. First, to take into account the dynamic characteristics of the UAM, a dynamic model of the UAM with state-dependent uncertainties and external disturbances is introduced. Then, note that a priori bounded uncertainty may impose a priori constraint on the system state before obtaining closed-loop stability. To remove this assumption, an ASMDO with a nested adaptive structure is introduced to effectively estimate and compensate the external disturbances and state-dependent uncertainties in finite time without the information of the upper bound of the uncertainties and disturbances and their derivatives. Furthermore, based on the proposed ASMDO, the finite-time control scheme with the prescribed performance is presented to ensure finite-time convergence and implement the specified transient and steady-state performance. The Lyapunov tools are utilized to analyze the stability of the proposed controller. Finally, the correctness and performance of the proposed controller are illustrated through numerical simulation comparisons and outdoor experimental comparisons.

Adaptive control for a payload carrying spacecraft with state constraints

In this article, a novel adaptive trajectory tracking controller is designed for a payload-carrying spacecraft under full state constraints. The proposed controller can tackle state-dependent uncertainties without a priori knowledge of their structures and upper bounds. The controller ensures time-varying constraints on all states and their time derivatives. The closed-loop stability of the proposed scheme is verified analytically via the Lyapunov method, and real-life experiments using a robotic testbed validated the effectiveness of the proposed adaptive controller over the state-of-the-art.

Persistently Feasible Robust Safe Control by Safety Index Synthesis and Convex Semi-Infinite Programming

Model mismatches prevail in real-world applications. Ensuring safety for systems with uncertain dynamic models is critical. However, existing robust safe controllers may not be realizable when control limits exist. And existing methods use loose over-approximation of uncertainties, leading to conservative safe controls. To address these challenges, we propose a control-limits aware robust safe control framework for bounded state-dependent uncertainties. We propose safety index synthesis to find a robust safe controller guaranteed to be realizable under control limits. And we solve for robust safe control via Convex Semi-Infinite Programming, which is the tightest formulation for convex bounded uncertainties and leads to the least conservative control. In addition, we analyze when and how safety can be preserved under unmodeled uncertainties. Experiment results show that our robust safe controller is always realizable under control limits and is much less conservative than strong baselines.

Adaptive Control of Euler-Lagrange Systems under Time-varying State Constraints without a Priori Bounded Uncertainty

In this article, a novel adaptive controller is designed for Euler-Lagrangian systems under predefined time-varying state constraints. The proposed controller could achieve this objective without a priori knowledge of system parameters and, crucially, of state-dependent uncertainties. The closed-loop stability is verified using the Lyapunov method, while the overall efficacy of the proposed scheme is verified using a simulated robotic arm compared to the state of the art.

A predictive safety filter for learning-based control of constrained nonlinear dynamical systems

The transfer of reinforcement learning (RL) techniques into real-world applications is challenged by safety requirements in the presence of physical limitations. Most RL methods, in particular the most popular algorithms, do not support explicit consideration of state and input constraints. In this paper, we address this problem for nonlinear systems with continuous state and input spaces by introducing a predictive safety filter, which is able to turn a constrained dynamical system into an unconstrained safe system and to which any RL algorithm can be applied ‘out-of-the-box’. The predictive safety filter receives the proposed control input and decides, based on the current system state, if it can be safely applied to the real system, or if it has to be modified otherwise. Safety is thereby established by a continuously updated safety policy, which is based on a model predictive control formulation using a data-driven system model and considering state and input dependent uncertainties.

A predictive approach to adaptive fuzzy sliding-mode control of under-actuated nonlinear systems with input saturation

In this paper, a computationally efficient robust predictive control method is proposed for continuous-time under-actuated SISO systems in the presence of actuator saturation and state-dependent uncertainties. The proposition of this research is to employ the idea of model prediction together with the Adaptive Fuzzy Sliding-Mode Control (AFSMC) for tuning the sliding surface parameters by predicting the anticipated effects of uncertainties. In the proposed scheme, only after the trigger conditions are met, the coefficients of the sliding surface are updated and the AFSMC is applied. Hence, computational complexity can be controlled by adjusting the switching rule. In the AFSMC, a fuzzy system is used to approximate a nonlinear function, and a robust term to compensate for any possible mismatches. An adaptively tuned gain is also applied to the control signal to prevent instability caused by the actuator saturation. Based on the updating sliding surface, fuzzy singletons, the upper bound of the fuzzy approximation error, and the saturation gain are adaptively tuned. Closed-loop stability is shown to be guaranteed using the multiple Lyapunov functions theorem and the Barbalat’s lemma. Finally, the method is applied for the depth control of an Autonomous Underwater Vehicle (AUV), depicting the excellent performance of the proposed method.

Adaptive stochastic model predictive control of linear systems using Gaussian process regression

This paper presents a stochastic model predictive control method for linear time-invariant systems subject to state-dependent additive uncertainties modelled by Gaussian process (GP). The new method is developed by re-building the tube-based model predictive control framework with chance constraints via adaptive constraint tightening. In particular, the tightened constraint set is constructed by forecasting the confidence region of uncertainty. Utilising this adaptive strategy, the Gaussian process based stochastic model predictive control (GP-SMPC) algorithm is designed by applying the adaptive tightened constraints in all prediction horizons. To reduce the computation load, the one-step GP-SMPC algorithm is further developed by imposing the tightened constraints only to the first-step nominal state and the worst-case constraints to the remaining steps. Under the assumption that the state-dependent uncertainties are bounded, the recursive feasibility of the designed optimisation problem is ensured, and the closed-loop system stability is guaranteed. The effectiveness and advantage over existing methods are verified via simulation and comparison studies.

Decentralized Adaptive Event-Triggered Control for a Class of Uncertain Systems With Deception Attacks and Its Application to Electronic Circuits

The problem of decentralized event-triggered control for a class of network-based state-dependent uncertain systems subject to network transmission delay and deception attacks is considered in this article. To reduce network load, a novel decentralized adaptive event-triggered scheme (AETS) is developed to transmit necessary sampled signals. During network transmission, a more practical deception attack phenomenon is considered, where the attack behaviors in different channels are governed by independent Bernoulli processes. Moreover, a set of improved data buffers are applied in the controller side to organize the decentralized triggered data and alleviate the impact of network transmission delay, such that the transmitted data can be utilized timely. Then, an integrated closed-loop system with state-dependent uncertainties is constructed by taking the AETS, deception attacks and data buffers into account. Sufficient conditions that guarantee the mean-square exponential stability of the closed-loop system are presented by employing the Lyapunov functional method, and the design criterion of the controller gain is given by an exact expression. Finally, the proposed method is applied to the control of electronic circuits to verify its practicability and effectiveness.

H ∞ Time-Delayed Fractional Order Adaptive Sliding Mode Control for Two-Wheel Self-Balancing Vehicles.

In this paper, a time-delayed fractional order adaptive sliding mode control algorithm is proposed for a two-wheel self-balancing vehicle system. The closed-loop system is proved based on the Lyapunov-Razumikhin function. The switching function is designed to make the system robust when facing uncertainties and external disturbances. It is designed to avoid monotonically increasing gains and can handle state-dependent uncertainties without a prior bound. The two-wheel self-balancing vehicle used in the experiment consists of a gyroscope MPU-6050 and accelerometer, a motor driving circuit composed of a motor driving chip TB6612FNG, and STM32F103x8B that is selected as the control core. The experimental results show that the time-delayed fractional order adaptive sliding mode control algorithm can make the vehicle achieve autonomous balance and quickly restore its stable state while appropriate disturbance is introduced.

Towards structure-independent stabilization for uncertain underactuated Euler–Lagrange systems

Available control methods for underactuated Euler–Lagrange (EL) systems rely on structure-specific constraints that may be appropriate for some systems, but restrictive for others. A generalized (structure-independent) control framework is to a large extent missing, especially in the presence of uncertainty. This paper introduces an adaptive-robust control framework for a quite general class of uncertain underactuated EL systems. Compared to existing literature, the important attributes of the proposed solution are: (i) avoiding structure-specific restrictions, namely, symmetry condition property of the mass matrix, and a priori bounds on non-actuated states or state derivatives; (ii) considering Coriolis, centripetal, friction and gravity terms to be unknown, while only requiring the knowledge of maximum perturbation around a nominal value of the mass matrix; (iii) handling state-dependent uncertainties irrespective of their linear or nonlinear in parameters structure. These features significantly widen the range of underactuated EL systems the proposed solution can handle in comparison to the available methods. Stability is studied analytically and the performance is verified in simulation using offshore boom crane dynamics.

Robust adaptive prescribed-time stabilization via output feedback for uncertain nonlinear strict-feedback-like systems

While control design objectives are formulated most commonly in terms of asymptotic behavior (as time goes to infinity) of signals in the closed-loop system, the recently developed notion of “prescribed-time” stabilization considers closed-loop signal behavior over a fixed (prescribed) time interval and addresses the problem of regulating the state to the origin in the prescribed time irrespective of the initial state. While prior results on prescribed-time stabilization considered a chain of integrators with uncertainties matched with the control input (i.e., normal form), we consider here a general class of nonlinear strict-feedback-like systems with state-dependent uncertainties allowed throughout the system dynamics including uncertain parameters (without requirement of any known bounds on the uncertain parameters). Furthermore, we address the output-feedback problem and show that a dynamic observer and controller can be designed based on our dual dynamic high gain scaling based design methodology along with a novel temporal transformation and form of the scaling dynamics with temporal forcing terms to achieve both state estimation and regulation in the prescribed time.

Adaptive control for autonomous ships with uncertain model and unknown propeller dynamics

Motion control is one of the most critical aspects in the design of autonomous ships. During maneuvering, the dynamics of propellers as well as the craft hydrodynamical specifications experience severe uncertainties. In this paper, an adaptive control approach is proposed to control the motion and trajectory tracking of an autonomous vessel by adopting neural networks that is used for estimating the dynamics of the propellers and handling hydrodynamical uncertainties. Considering that the maneuvering model of a vessel resemble a nonlinear non-affine-in-control system, the proposed neural-based adaptive control algorithm is designed to estimate the nonlinear influence of the input function which in this case is the dynamics of propellers and thrusters. It is also shown that the proposed methodology is capable of handling state dependent uncertainties within the ship maneuvering model. A Lyapunov-based technique and Uniform Ultimate Boundedness are used to prove the correctness of the algorithm. To assess the method’s performance, several experiments are considered including trajectory tracking simulations in the port of Rotterdam.

Hybrid position/force control of Stewart Manipulator using Extended Adaptive Fuzzy Sliding Mode Controller (E-AFSMC)

A new and effective control method is proposed for the hybrid position/force control of a Stewart Manipulator (SM). The control approach can be divided into the two parts, the first is an estimation of contact parameters between the robot and environment and the second one is the force control of manipulator according to estimated parameters. Hunt–Crossley nonlinear model is considered to describe the normal force in the contact region and Modified Extended Kalman Filter (MEKF) is used for estimating contact parameters. Extended Adaptive Fuzzy Sliding Mode Controller (E-AFSMC) is designed to hybrid position/force control of SM in the presence of state-dependent uncertainties. The proposed method is verified numerically, showing the effectiveness of the proposed method in critical situations such as actuator saturation, unexpected large disturbances, and state-dependent uncertainties.

Iterative learning control for boundary tracking of uncertain nonlinear wave equations

This work presents a framework of iterative learning control (ILC) design for a class of nonlinear wave equations. The main contribution lies in that it is the first time to extend the idea of well-established ILC for lumped parameter systems to boundary tracking control of nonlinear hyperbolic distributed parameter systems (DPSs). By fully utilizing the system repetitiveness, the proposed control algorithm is capable of dealing with time-space-varying and even state-dependent uncertainties. The convergence and robustness of the proposed ILC scheme are analyzed rigorously via the contraction mapping methodology and differential/integral constraints without any system dynamics simplification or discretization. In the end, two examples are provided to show the efficacy of the proposed control scheme.

Fixed-time consensus of complex dynamical networks with nonlinear coupling and fuzzy state-dependent uncertainties

In this paper, the fixed-time consensus problem for complex dynamical networks with nonlinear coupling and fuzzy state-dependent uncertainties is discussed. Different from most existing publications, the controller is designed as a fuzzy logic system, which is applicable for complex dynamical networks with system uncertainties and unknown topology to ensure the fixed-time consensus. Furthermore, compared with the initial-condition based finite-time consensus, the settling time is bounded by a constant within fixed-time regardless of the initial condition. Based on the Lyapunov stability theory and inequality techniques, some sufficient criteria for fixed-time consensus are obtained. Finally, two numerical examples are granted to display the performance of the obtained results.

New AFSMC Method for Nonlinear System with State-dependent Uncertainty: Application to Hexapod Robot Position Control

Conventional Adaptive Fuzzy Sliding Mode Control (AFSMC) method is extended for nonlinear affine systems with state-dependent upper bound of uncertainties. More general affine model of the system with state-dependent uncertainties is proposed where such a model is more applicable in robotics. Position control of a Stewart Manipulator (SM) is then considered as a challenging case study to experimentally verify the effectiveness of the proposed Extended AFSMC (E-AFSMC) method. The proposed method is encompassed of a fuzzy system for estimation of a nonlinear system, a robust controller for compensation of uncertainties and some appropriate adaptation laws for optimization of performance. The second Lyapunov theorem and Barbalat lemma are used to prove the closed-loop asymptotic stability. Furthermore, numerical simulations depict the robustness of the proposed controller and in particular, under the very critical situation of actuator saturation and unexpected uncertainties. The effectiveness of the proposed control method is validated through experimental results.

Learning-Based Robust Model Predictive Control with State-Dependent Uncertainty

Abstract A robust model predictive control (RMPC) approach for linear systems with bounded state-dependent uncertainties is proposed. Such uncertainties can arise from unmodeled non-linearities or external disturbances, for example. By explicitly considering the state dependency of the uncertainty sets in the RMPC approach, it is shown how closed-loop performance can be improved over existing approaches that consider worst-case uncertainty. Being able to handle state-dependent uncertainties is particularly relevant in learning-based MPC where the system model is learned from data and confidence in the model typically varies over the state space. The efficacy of the proposed approach for learning-based RMPC is illustrated with a numerical example, where uncertainty sets are obtained from data using Gaussian Process regression.