Initial Control Input Research Articles

Prescribed-Time Output Feedback Control for Cyber-Physical Systems Under Output Constraints and Malicious Attacks.

This article presents a prescribed-time output feedback control (PTOFC) algorithm for cyber-physical systems (CPSs) under output constraint occurring in any finite time interval (OC-AFT) and malicious attacks. The OC-AFT meaning that the output constraint only occurs during a finite number of time periods while being absent in others, which is more general and complex than traditional infinite-time/deferred output constraints. A stretch model-based nonlinear mapping function is constructed to handle the OC-AFT, and a salient advantage is that the proposed algorithm is also suit for CPSs with infinite-time/deferred output (or funnel) constraints, as well as those that are constraint-free, without necessitating changes to the control structure. The uncertain terms (including system model uncertainties, malicious attacks, and external disturbances) are compensated by fuzzy logic systems. Furthermore, a novel practical prescribed-time stability criterion is proposed, under which a novel PTOFC scheme is given. The results demonstrate that the proposed scheme can ensure that both tracking error and observation error converge to a neighborhood centered on zero within a prescribed time, while accommodating the OC-AFT and malicious attacks. Additionally, the settling time remains unaffected by control parameters and initial states, and the limitations of excessive initial control inputs and singularity problems in existing prescribed-time control algorithms are eliminated. The developed algorithm is exemplified through simulation instances.

Three-dimensional terminal angle constraint guidance law with class [formula omitted] function-based adaptive sliding mode control

This paper investigates the three-dimensional (3-D) interception guidance problem, where the missile is required to intercept the maneuvering target with the desired terminal angles. For the nonlinear relative kinematic model, a class K∞ function-based adaptive sliding mode guidance law is proposed, which ensures that the errors of terminal Line-of-Sight (LOS) angles converge to the small neighborhoods of origin at the time of interception, without relying on information about the target's acceleration. To overcome the challenges of large initial control input and chattering in existing sliding mode guidance laws, two improved control schemes are introduced. The first scheme is to directly impose saturation constraints into the adaptive gain. However, it is important to ensure that the unknown disturbance remains within the prescribed saturation bound. To avoid the limitation, another approach involves introducing auxiliary dynamics to eliminate the reaching phase and slow down the convergence of LOS angles by presetting the convergence time of the sliding mode variables, which helps mitigate excessive initial control inputs. Numerical simulations are conducted using a realistic missile model and considering a 3-DOF point-mass aircraft as the target to evaluate three different guidance laws. The results indicate that the proposed guidance law ensures interception accuracy while substantially reducing the control gain.

Adaptive prescribed finite-time asymptotic tracking control for switched systems with unknown initial conditions and full-state constraints

In this paper, an adaptive prescribed finite-time asymptotic tracking control problem is considered for the unknown nonlinear switched systems with unknown initial conditions and full-state constraints. A class of nonlinear mappings (NMs) and a new prescribed finite-time performance function (PFTPF) are introduced so that the control design is independent of initial conditions of the controlled states. Based on the neural network approximation approach, NMs, PFTPF and the Barbalat's lemma, an adaptive prescribed finite-time asymptotic tracking controller with full-state constraints is obtained. To avoid overlarge initial control input, the design method with zero initial control input is adopted, the definition of input tuning function (ITF) is expanded and its effectiveness is proved theoretically. As results, the full-state constraints and the boundedness of all the signals in the closed-loop system are guaranteed, and the tracking error of the system can converge to zero asymptotically. Finally, the effectiveness and superiority of the proposed scheme are verified by the simulation results.

Practical time-boundary consensus for fractional-order multi-agent systems under well-known and estimable topology

A framework for multi-agent systems with single-integrator dynamics to achieve practical fixed-time consensus has been developed under a well-known topology. However, the disagreement boundary in which is influenced by the initial values of the system. To avoid this, a practical time-boundary (PTB) consensus framework using a novel time-boundary-base generator (TBBG) is proposed in this paper, and it is extended to fractional-order multi-agent systems and estimable topology. A significant fractional differential equation is solved as the theoretical basis to achieve PTB consensus. Evolving from the time-base generator, this novel TBBG inherits the benefit of reducing the initial control input and saves energy consumption by optimizing four newly added adjustable parameters compared to the existing work. Additionally, outcomes are extended to quasi-PTB consensus and PTB-cluster consensus. The effectiveness and superiorities of the proposed approach are illustrated by two numerical examples.

Model-free algorithm for consensus of discrete-time multi-agent systems using reinforcement learning method

In this work, we investigate consensus issues of discrete-time (DT) multi-agent systems (MASs) with completely unknown dynamic by using reinforcement learning (RL) technique. Different from policy iteration (PI) based algorithms that require admissible initial control policies, this work proposes a value iteration (VI) based model-free algorithm for consensus of DTMASs with optimal performance and no requirement of admissible initial control policy. Firstly, in order to utilize RL method, the consensus problem is modeled as an optimal control problem of tracking error system for each agent. Then, we introduce a VI algorithm for consensus of DTMASs and give a novel convergence analysis for this algorithm, which does not require admissible initial control input. To implement the proposed VI algorithm to achieve consensus of DTMASs without information of dynamics, we construct actor-critic networks to online estimate the value functions and optimal control inputs in real time. At last, we give some simulation results to show the validity of the proposed algorithm.

Simultaneous moving horizon estimation and control for nonlinear systems subject to bounded disturbances

SummaryIn this work, we address the output–feedback control problem for nonlinear systems under bounded disturbances using a moving horizon approach. The controller is posed as an optimisation‐based problem that simultaneously estimates the state trajectory and computes future control inputs. It minimizes a criterion that involves finite backward and forward horizons with respect to the unknown initial state, measurement noises and control input variables. The main novelty of this work relies on linking the lengths of the forward and backward windows with the closed‐loop stability, assuming detectability and decoding sufficient conditions to assure system stabilizability. It leads to a formulation that does not require to be a Control Lyapunov Function for the terminal cost of the controller. Simulation examples are carried out to compare the performance of solving simultaneously and independently the estimation and control problems. Furthermore, the examples show how the controller influences the length of the estimation window through its gain.

An explicit-time and explicit-accuracy control for a state-constrained nonstrict-feedback uncertain system based on adaptive fuzzy dynamic-approximation

This article proposes a novel explicit-time and explicit-accuracy adaptive fuzzy control for a state-constrained nonlinear nonstrict-feedback uncertain system. This method can explicitly parameterize the upper bound of settling-time with low initial control input under a bounded initial condition. Meanwhile, this method can also explicitly parameterize the upper bound of accuracy while achieving low control input based on the adaptive fuzzy dynamic-approximation theorem. Firstly, a novel generalized explicit-time stability system is proposed by introducing the boundary gain term to render the time-parameter explicit, this method can solve the input conservatism problem caused by the unbounded-state gain term of traditional fixed/prdefined-time function. Then, according to the universal fuzzy approximation theorem, the novel dynamic relationship of adaptive fuzzy logic system between approximation error and adaptive parameters is presented. This relationship can lead to the adaptive fuzzy dynamic-approximation theorem, and an adaptive law designed by this theorem can realize the Lyapunov stability of adaptive control system under a Lasalle invariant set. In the end, a novel adaptive fuzzy control scheme is proposed by the generalized explicit-time function and adaptive fuzzy dynamic-approximation theorem. This scheme can achieve the explicit-time stability by the human-like activation function, and the accuracy can be parameterized by Lyapunov synthesis. Compared with other existing fixed/prdefined-time adaptive fuzzy control methods, the proposed explicit-time and explicit-accuracy controller achieves a significant reduction in the initial control input. Theoretical analysis and simulation results validate the effectiveness of the proposed method.

A prescribed-performance-based adaptive finite-time tracking control scheme circumventing the dependence on the system initial condition

This paper is concerned with the prescribed finite-time tracking control problem for a class of nonlinear systems with unknown initial condition, state time-varying delays and external disturbances. A new adaptive prescribed finite-time tracking control scheme bypassing system initial condition is proposed via the prescribed performance method. Several nonlinear mapping functions (NMFs) and a new prescribed finite-time performance function (PFTPF) combining finite-time control with prescribed performance control are constructed to obtain the scheme. In this paper, the assumptions on the time-delay terms are removed by means of the designed Lyapunov–Krasovskii functions. In addition, to avoid step impact effect arisen by an overlarge initial control input, a control input with zero initial value is obtained. Aiming at the design of zero initial control input, a new Lyapunov stability criterion form is put forward. Two practical examples are presented to confirm the effectiveness and superiority of the proposed scheme.

Fixed-Time and Prescribed-Time Consensus Control of Multiagent Systems and Its Applications: A Survey of Recent Trends and Methodologies

Fixed-time and prescribed-time consensus control can bring an explicit estimate of the settling time without dependence on initial conditions, which is important in providing control engineers <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> system information. This article aims at presenting a survey of recent trends and methodologies of fixed-time and prescribed-time consensus control in multiagent systems. First, some typical fixed-time consensus results are reviewed. Despite the advantage in deriving a fixed settling time bound, fixed-time consensus controllers usually result in a conservative estimate of the bound and a large magnitude of initial control input, which in turn show the necessity of designing prescribed-time consensus controllers. Second, characteristics and controller design of (practical, respectively) prescribed-time consensus are provided in detail. Particularly, representative time-varying function-based controllers are presented, by which (practical, respectively) consensus can be achieved in prescribed time. Third, applications of fixed-time and prescribed-time consensus control in mobile robots and smart grids are illustrated in case studies. Finally, several challenging issues in prescribed-time consensus control are discussed for future research.

Domain-aware Control-oriented Neural Models for Autonomous Underwater Vehicles

Conventional physics-based modeling is a time-consuming bottleneck in control design for complex nonlinear systems like autonomous underwater vehicles (AUVs). In contrast, purely data-driven models require a large number of observations and lack operational guarantees for safety-critical systems. Data-driven models leveraging available partially characterized dynamics have potential to provide reliable systems models in a typical data-limited scenario for high value complex systems, thereby avoiding months of expensive expert modeling time. In this work we explore this middle-ground between expert-modeled and pure data-driven modeling. We present control-oriented parametric models with varying levels of domain-awareness that exploit known system structure and prior physics knowledge to create constrained deep neural dynamical system models. We employ universal differential equations to construct data-driven blackbox and graybox representations of the AUV dynamics. In addition, we explore a hybrid formulation that explicitly models the residual error related to imperfect graybox models. We compare the prediction performance of the learned models for different distributions of initial conditions and control inputs to assess their suitability for control.

A local dynamic extreme learning machine based iterative learning control of nonlinear batch process

AbstractThis article deals with the optimal control issue of nonlinear batch process. First, in order to derive high efficiency and accuracy process model, a novel hierarchical searching mechanism local dynamic nonlinear model is constructed which is composed of just‐in‐time learning and extreme learning machine (JITL‐ELM). Then, based on the local dynamic JITL‐ELM model, an optimal quadratic‐criterion‐based iterative learning control (Q‐ILC) algorithm is presented, where the control input trajectory can be obtained by solving a quadratic programming problem. Moreover, on the basis of inverse model system, the initial batch control input trajectory of the Q‐ILC algorithm can be obtained by the use of JITL method. As a result, not only the issue of model‐plant mismatch and real‐time disturbance can be solved, but also obtain faster system convergence rate and smaller tracking error. Besides, the convergence properties of control input and tracking error are analyzed. Finally, a typical batch process is presented to demonstrate the feasibility and superiority.

Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations

This work derives a residual-based a posteriori error estimator for reduced models learned with non-intrusive model reduction from data of high-dimensional systems governed by linear parabolic partial differential equations with control inputs. It is shown that quantities that are necessary for the error estimator can be either obtained exactly as the solutions of least-squares problems in a non-intrusive way from data such as initial conditions, control inputs, and high-dimensional solution trajectories or bounded in a probabilistic sense. The computational procedure follows an offline/online decomposition. In the offline (training) phase, the high-dimensional system is judiciously solved in a black-box fashion to generate data and to set up the error estimator. In the online phase, the estimator is used to bound the error of the reduced-model predictions for new initial conditions and new control inputs without recourse to the high-dimensional system. Numerical results demonstrate the workflow of the proposed approach from data to reduced models to certified predictions.

Stability Control of a Biped Robot on a Dynamic Platform Based on Hybrid Reinforcement Learning.

In this work, we introduced a novel hybrid reinforcement learning scheme to balance a biped robot (NAO) on an oscillating platform, where the rotation of the platform is considered as the external disturbance to the robot. The platform had two degrees of freedom in rotation, pitch and roll. The state space comprised the position of center of pressure, and joint angles and joint velocities of two legs. The action space consisted of the joint angles of ankles, knees, and hips. By adding the inverse kinematics techniques, the dimension of action space was significantly reduced. Then, a model-based system estimator was employed during the offline training procedure to estimate the dynamics model of the system by using novel hierarchical Gaussian processes, and to provide initial control inputs, after which the reduced action space of each joint was obtained by minimizing the cost of reaching the desired stable state. Finally, a model-free optimizer based on DQN (λ) was introduced to fine tune the initial control inputs, where the optimal control inputs were obtained for each joint at any state. The proposed reinforcement learning not only successfully avoided the distribution mismatch problem, but also improved the sample efficiency. Simulation results showed that the proposed hybrid reinforcement learning mechanism enabled the NAO robot to balance on an oscillating platform with different frequencies and magnitudes. Both control performance and robustness were guaranteed during the experiments.

Walking Control of a Biped Robot on Static and Rotating Platforms Based on Hybrid Reinforcement Learning

In this paper, we proposed a novel Hybrid Reinforcement Learning framework to maintain the stability of a biped robot (NAO) while it is walking on static and dynamic platforms. The reinforcement learning framework consists of the Model-based off-line Estimator, the Actor Network Pre-training scheme, and the Mode-free on-line optimizer. We proposed the Hierarchical Gaussian Processes as the Mode-based Estimator to predict a rough model of the system and to obtain the initial control input. Then, the initial control input is employed to pre-train the Actor Network by using the initial control input. Finally, a model-free optimizer based on Deep Deterministic Policy Gradient framework is introduced to fine tune the Actor Network and to generate the best actions. The proposed reinforcement learning framework not only successfully avoids the distribution mismatch problem while combining model-based scheme with model-free structure, but also improves the sample efficiency for the on-line learning procedure. Simulation results show that the proposed Hybrid Reinforcement Learning mechanism enables the NAO robot to maintain balance while walking on static and dynamic platforms. The robustness of the learned controllers in adapting to platforms with different angles, different magnitudes, and different frequencies is tested.

Practical fixed-time consensus for integrator-type multi-agent systems: A time base generator approach

A new practical fixed-time consensus framework for integrator-type multi-agent systems is developed by using a time base generator (TBG). For both leaderless and leader-following consensus, new TBG-based protocols are proposed for the multi-agent systems. The resulting settling time can be pre-designated without dependence on initial states. Different from some conventional fixed-time consensus strategies, where the magnitude of initial control input is large, the proposed TBG-based protocols significantly reduce the magnitude, which is demonstrated through comparison studies using illustrative examples.

Application of optimal control theory based on the evolution strategy (CMA-ES) to automatic berthing

To realize autonomous ships in the near future, possibility of automatic berthing has been investigated. Automatic berthing is not an easy task because of some complexities that are included in the problem, such as the nonlinearity of the low-speed maneuvering model, danger of collision with berth, etc. In this research, as a first step, the authors solved the off-line automatic berthing problem. Here, the optimal control problem was modeled as minimum-time problem, and the collision risk with the berth was taken into account. The authors attempted to apply the covariance matrix adaption evolution strategy (CMA-ES), which is considered state-of-the-art in evolutionary computation approaches for optimization of real-valued variables. In the problem dealt with here, a propeller and a rudder were used only as control inputs; so, the degree of difficulty was significantly high. Nevertheless, optimal control method based on the CMA-ES successfully gave us the offline results for typical situations considered. It is noteworthy that preparation of a feasible initial control input was not required in the calculation process, which made the proposed procedure robust. The calculation method proposed here is offline, but the results could be applied as an initial guess in an online (real-time) control problem.

An improved adaptive fuzzy backstepping control for nonlinear mechanical systems with mismatched uncertainties

ABSTRACTWhen the nonlinear mechanical system has mismatched uncertainties, it is difficult to design control algorithm to achieve high precision trajectory tracking control. Traditional backstepping control is an effective control method for uncertain, mismatched nonlinear systems, but there is inherent problem of “complexity due to the explosion of terms”. In this paper, based on the backstepping method, only one fuzzy system is used to approximate the unknown nonlinear functions, the unknown control gain and the differential of virtual control law of each subsystem. In order to reduce the influence of fuzzy approximation error and external interference, the above control scheme is further improved by designing special adjustable control parameters and first order low pass filter. The improved control scheme not only improves the control precision of the system obviously, but also solves the problem of “explosion of terms”, and greatly reduces the initial control input, and provides the conditions for the practical application. The simulation results show the effectiveness of the proposed methods.

Real-time optimization of the key filtration parameters in an AnMBR: Urban wastewater mono-digestion vs. co-digestion with domestic food waste

This study describes a model-based method for real-time optimization of the key filtration parameters in a submerged anaerobic membrane bioreactor (AnMBR) treating urban wastewater (UWW) and UWW mixed with domestic food waste (FW). The method consists of an initial screening to find out adequate filtration conditions and a real-time optimizer applied to a periodically calibrated filtration model for minimizing the operating costs. The initial screening consists of two statistical analyses: (1) Morris screening method to identify the key filtration parameters; (2) Monte Carlo method to establish suitable initial control inputs values. The operating filtration cost after implementing the control methodology was €0.047 per m3 (59.6% corresponding to energy costs) when treating UWW and €0.067 per m3 when adding FW due to higher fouling rates. However, FW increased the biogas productivities, reducing the total costs to €0.035 per m3. Average downtimes for reversible fouling removal of 0.4% and 1.6% were obtained, respectively. The results confirm the capability of the proposed control system for optimizing the AnMBR performance when treating both substrates.

A New Fuzzy Iterative Learning Control Algorithm for Single Joint Manipulator

Abstract This paper present a new fuzzy iterative learning control design to solve the trajectory tracking problem and performing repetitive tasks for rigid robot manipulators. Several times’ iterations are needed to make the system tracking error converge, especially in the first iteration without experience. In order to solve that problem, fuzzy control and iterative learning control are combined, where fuzzy control is used to tracking trajectory at the first learning period, and the output of fuzzy control is recorded as the initial control inputs of ILC. The new algorithm also adopts gain self-tuning by fuzzy control, in order to improve the convergence rate. Simulations illustrate the effectiveness and convergence of the new algorithm and advantages compared to traditional method.

Approximate local output regulation for nonlinear distributed parameter systems

Output regulation for a class of nonlinear infinite-dimensional systems, called regular nonlinear systems (RNS), is the subject of this work. For the plants in this class, the linearization at the origin is an exponentially stable regular linear system (RLS). The plants are driven by a control input and a disturbance signal. Well-posedness of the plants for small initial states, control inputs and disturbance signals is established and it is shown that if the control input and the disturbance signal for a plant are T-periodic, then so are its state and output (asymptotically). On the basis of this characterization, an approximate local output regulator problem for multi-input multi-output (MIMO) plants in the RNS class is addressed. Given a plant, the regulation objective is to ensure that a finite number of harmonics of a T-periodic reference signal and the plant output are identical whenever the reference signal, the T-periodic disturbance signal for this plant and the initial state are small. An internal model based output feedback control scheme is proposed for an exponentially stable RLS for tracking reference signals, which are a finite sum of functions that are a product of a sinusoid and a polynomial in time. This scheme merely uses the transfer function gains of the RLS at the poles of the Laplace transform of the reference signal and practically requires no other data. Using the proposed control scheme, a linear finite-dimensional controller is designed for a MIMO nonlinear plant in the RNS class using minimal plant information. The resulting closed-loop system is rigorously analyzed to establish that the controller achieves the regulation objective. The efficacy of the control design is illustrated numerically using the model of a cable coupled to a point mass via a nonlinear spring.