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Consider a positive functional F ⁢ ( y ) := ∫ t T L ⁢ ( s , y ⁢ ( s ) , y ′ ⁢ ( s ) ) ⁢ 푑 s {F(y):=\int_{t}^{T}L(s,y(s),y^{\prime}(s))\,ds} , defined on the space of Sobolev functions W 1 , p ⁢ ( [ t , T ] ; ℝ n ) {W^{1,p}([t,T];{\mathbb{R}}^{n})} , where p ≥ 1 {p\geq 1} . This functional is minimized among functions y that may satisfy one or both endpoint conditions. The Lagrangian L is allowed to assume the value + ∞ {+\infty} . In numerous applications minimizers may not be explicit or even may not exist. In such circumstances, it is crucial to know that the infimum of F can be approximated using a sequence of Lipschitz functions that meet the given boundary conditions. However, there are instances where this approximation is not feasible, even with polynomial Lagrangians that meet Tonelli’s existence conditions: this situation is referred to as the Lavrentiev phenomenon. Some results are present in the literature if one requires the Lipschitz approximations to preserve just one endpoint constraint or when the Lagrangian is finite valued. The present paper deals with problems with two endpoint constraints and Lagrangians that are allowed to take extended values. As a byproduct, our Lipschitz approximations may preserve given state constraints. The extended-valued case is challenging since the phenomenon may occur even when the Lagrangian is constant on its effective domain, whose topology becomes relevant. Once assumed that the Lagrangian is radial convex on the rays of the last variable, our findings offer new insights, even when the Lagrangian L is real-valued, autonomous, and there are no state constraints. [ABSTRACT FROM AUTHOR]

This paper deals with the output voltage tracking problem in DC-DC boost converters under the single-loop structure, emphasizing the need for overcurrent protection. Overcurrent protection is considered as a state constraint that is applied to the inductor current. A novel current-constrained controller is proposed by designing a special dynamic controller gain that is associated with the inductor current. Unlike existing nonlinear control methods capable of implementing state constraints, the controller introduced in this paper has a relatively simple structure that simplifies execution and reduces computational complexity. In contrast to methods that limit the initial states of the system, such as invariant set theory, the proposed method expands the range of the admissible set of the initial states. Experimental results demonstrate that, under the premise of satisfying current constraints, the proposed controller has better dynamic performance and robustness when compared to the nominal controllers that do not take current constraints into account. [ABSTRACT FROM AUTHOR]

To improve the following performance in large curve path and time-varying drift angle, a reduced-order extended state observer is added to the Improved Stanley Guidance Law (EISGL). Combining with the dynamic surface control (DSC), an adaptive auxiliary system is simultaneously built to compensate for the effect of the state constraints on the system. A barrier Lyapunov function combined with a prescribed performance function is designed to constrain the heading angle error of path following. Adaptive laws are also designed to approximate errors, estimating perturbation in poor sea condition. Lyapunov stability analysis shows that all signals are semi-global coherent and eventually bounded. In conclusion, the numerical comparison simulation experiments verify that the scheme has a strong anti-jamming capability and achieves good path following in large curve path. [ABSTRACT FROM AUTHOR]

This research proposes a novel BLF-based backstepping controller for path tracking of Autonomous Vehicles (AVs) with unknown dynamics and unmeasurable states. The proposed framework includes: (1) forming geometric-dynamic model of the vehicle by combining the dynamics of the vehicle with the kinematics of the visual measurement system, (2) designing a fixed-time Extended-State Observer (ESO) to estimate the unknown dynamics and unmeasurable states, and (3) introducing a BLF-based controller for faster response and more accurate path tracking compared to previous BLF-based controllers. Besides the novelty of the BLF-based controller, by transforming the closed-loop error dynamics into a unified proportional-derivative (PD)-type structure, an intuitive criterion is proposed to provide a systematic procedure for comparing BLF-based controllers. A combined BLF is further proposed based on this performance criterion to eliminate the sensitivity of BLF-based controllers to the magnitude of the constraint. The stability analysis is performed for the fixed-time ESO and the closed-loop control system. MATLAB/CarSim co-simulation is conducted to evaluate the performance of the proposed control system. The outcomes of the work show that the closed-loop control system is exponentially stable. In addition, it can provide a faster response and result in more accurate path tracking compared to previous BLF-based control systems. [ABSTRACT FROM AUTHOR]

The paper is devoted to trajectory optimization for an inertial object moving in a plane with thrust bounded in magnitude in the presence of external forces. The aim is to maximize the longitudinal terminal velocity with the state constraint satisfied at each time to avoid a lateral collision with an obstacle. The linear tangent law is used as the basis for an algorithm that controls the direction of the thrust. Conditions for the existence of a solution are studied. Constraints on the initial lateral velocity and the time of the motion of the object are obtained. Since the linear tangent law violates the constraint for some motion times, a modified control law is proposed. A transcendental equation is obtained to find a critical value of time above which an undesired collision occurs. The corresponding conjecture is formulated, which allows us to eliminate the ambiguity that arises during the solution process. A method for solving the problem is presented and confirmed by numerical calculations. [ABSTRACT FROM AUTHOR]

This paper addresses the challenge of managing state constraints in vehicle platoons, including maintaining safe distances and aligning velocities, which are key factors that contribute to performance degradation in platoon control. Traditional platoon control strategies, which rely on a constant time-headway policy, often lead to deteriorated performance and even instability, primarily during dynamic traffic conditions involving vehicle acceleration and deceleration. The underlying issue is the inadequacy of these methods to adapt to variable time-delays and to accurately modulate the spacing and speed among vehicles. To address these challenges, we propose a dynamic adjustment neural network (DANN) based cooperative control scheme. The proposed strategy employs neural networks to continuously learn and adjust to time varying conditions, thus enabling precise control of each vehicle’s state within the platoon. By integrating a DANN into the platoon control system, we ensure that both velocity and inter-vehicular spacing adapt in response to real-time traffic dynamics. The efficacy of our proposed control approach is validated using both Lyapunov stability theory and numeric simulation, which confirms substantial gains in stability and velocity tracking of the vehicle platoon.

The article proposes a state-saturated-like second-order sliding mode (SOSM) algorithm to tackle the state constraint in permanent magnet synchronous motor system, which not only regulates the speed perfectly but also offers the maximum domain of attraction in the predefined state constraints. Unlike the traditional speed controller, the proposed controller is based on the SOSM control theory, and the saturation function is introduced in the design, which means that the controller has the better robustness and is capable of constraining the states, thereby mitigating the risk of excessive transient currents that may pose a threat to circuit safety. The stability of the proposed speed controller is fully proven using the Lyapunov theory. Finally, the validity of the proposed control scheme is verified through simulations and experiments. For a comparative study, three different control strategies, that is, the proposed control, proportional integral control, and conventional sliding mode control, are carried out to demonstrate the superiority of the proposal. These results indicate that the proposed algorithm exhibits the superior performance in terms of robustness, as well as in limiting startup transient current and ameliorating overshoot simultaneously. [ABSTRACT FROM AUTHOR]

Copyright of Systems Engineering & Electronics is the property of Journal of Systems Engineering & Electronics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper investigates the mathematical programming formulation of semilinear elliptic optimal control problems with finitely many state constraints, this allows the use of results in parametric mathematical programming. By applying recent stability results in parametric mathematical programming, we will obtain some new results on differential stability and tilt stability for parametric control problems. On the one hand, we derive an explicit upper estimate for regular subdifferential of marginal function of control problems under basic parameter perturbations. On the other hand, we establish a characterization of tilt stability of control problems under tilt parameter perturbations. [ABSTRACT FROM AUTHOR]

The problem of stabilizing the zero value of the state vector of constrained nonlinear dynamical systems written in a special form is solved. The proposed control design accounts for magnitude constraints on the values of state variables and is based on the integrator backstepping approach using logarithmic Lyapunov barrier functions. The obtained stabilizing feedbacks, in contrast to similar known results, are based on the use of linear virtual stabilizing functions that do not grow unboundedly as the state variables approach boundary values. As an example, we consider a state constraints aware solution of the control problem of positioning an autonomous underwater vehicle at a given point in space. [ABSTRACT FROM AUTHOR]

Accuracy of electro-mechanical actuator in aircraft is susceptible to variable operation conditions such as electromagnetic interference, changeable temperature or loss of maintenance, leading in turn to flight performance degradation. This paper proposed an unified control paradigm that aims to keep aircraft's velocity in a safe boundary and shorten the system stabilizing time in presence of actuator deviation. The controller is derived following a practical finite-time-convergence (FTC) with extended dynamics, and an integrated state-constraint structure so as to restrict air vehicle's attitude rate or translation velocity. It is proved that the system state converges to a sphere near the origin in a finite time, the state trajectory is always remain within the prescribed range, and all signals of the closed-loop system are uniformly ultimately bounded. Compared simulation with the quadratic Lyapunov-based FTC method and an asymptotic convergence controller are conducted on an unmanned helicopter prototype. Results show that the proposed controller enhances the dynamic and fault-tolerant performance of resisting actuator fluctuation. [ABSTRACT FROM AUTHOR]

This article investigates the leader–follower consensus problem of state-constrained flexible-joint manipulators. Many uncertainties exhibit in flexible-joint manipulators, which brings a great challenge to the leader–follower consensus control design, especially considering state constraints. In this work, a nonlinear state-dependent function is first constructed to deal with the full-state constraint problem. Then, a novel event-triggered adaptive fuzzy control strategy is presented by the function approximate technique, where a dynamic event-triggered mechanism is introduced to avoid continuous updates of the controller, and thereby control resources and communication burden can be effectively reduced. On the basis of Lyapunov stability analysis, it is proven that all error signals in the closed-loop systems are bounded, and the leader–follower consensus of flexible-joint manipulators is realized without violating full-state constraints. Simulation results and some comparisons are provided to validate the effectiveness of the presented control strategy. [ABSTRACT FROM AUTHOR]

In this article, a novel robust adaptive neural network tracking control scheme is presented for a class of uncertain nonlinear systems with quantized inputs and full state constraints. A tan-type barrier Lyaponov function is proposed to constrain all states, and the unknown nonlinear function term in virtual control is approximated by radial basis function neural network(RBFNN). The uncertainty term and disturbance term in the system are dealt with by robust scheme. Under the proposed quantized tracking control scheme, the communication load of the system is reduced, the boundedness of all signals in the closed-loop system is verified, the full state constraints are satisfied. Simulation results are presented to illustrate the effectiveness of the proposed adaptive control scheme.

The control of robot manipulator pose is significantly complicated by the uncertainties arising from flexible joints, presenting substantial challenges in incorporating practical operational constraints. These challenges are further exacerbated in teleoperation scenarios, where factors such as synchronization and external disturbances further amplify the difficulties. At the core of this research is the introduction of a pioneering teleoperation controller, ingeniously integrating a nonlinear extended state observer (ESO) with the barrier Lyapunov function (BLF) while effectively accommodating a steady time delay. The controller in our study demonstrates exceptional proficiency in accurately estimating uncertainties arising from both flexible joints and external disturbances using the nonlinear ESO. Refined estimates, in conjunction with operational constraints of the system, are integrated into our BLF-based controller. Consequently, a synchronized control mechanism for teleoperation is achieved, exhibiting promising performance. Importantly, our experimental findings provide substantial evidence that our proposed approach effectively reduces the tracking error of the teleoperation system to within 0.02 rad. This advancement highlights the potential of our controller in significantly enhancing the precision and reliability of teleoperated robot manipulators.

In flight control systems, the actuators need to tolerate aerodynamic torques and continue their operations without interruption. To this end, using the simulators to test the actuators in conditions close to the real flight is efficient. On the other hand, achieving the guaranteed performance encounters some challenges and practical limitations such as unknown dynamics, external disturbances, and state constraints in reality. Thus, this article attempts to present a robust adaptive neural network learning controller equipped with a disturbance observer for passive torque simulators (PTS) with load torque constraints. The radial basis function networks (RBFNs) are employed to identify the unknown terms, providing information for the disturbance observer. Besides, the tuning parameters are chosen optimally by adopting the grey wolf optimization (GWO) algorithm. The closed-loop system stability is also proven by the barrier Lyapunov function (BLF) while the total uncertainties, including system dynamics, friction, and disturbance, are tracked by the total estimation. Thus, the predetermined performance, robust behavior, and high-precision estimation are the achievements of the presented controller for PTS. To confirm the ability of the proposed control idea, simulations are provided. Furthermore, a comparison scenario is also considered to emphasize the supremacy of the proposed control system. [ABSTRACT FROM AUTHOR]

In this paper, a fractional optimal control problem with fractional Laplacian and integral state constraint is investigated. The first-order optimality system and regularity of the solutions to optimal control problem are derived. Piecewise linear finite element method combined with variational discretization approach is used to approximate the optimal control problem. A priori error estimates for finite element approximation of the state, adjoint state and control variable are derived. Numerical examples are given to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

An adaptive tracking control strategy with a prescribe tracking error and the convergence time is proposed for hypersonic vehicles with state constraints and actuator failures. The peculiarity is that constructing a new time scale coordinate translation mapping method, which maps the prescribe time on the finite field to the time variable on the infinite field, and the convergence problem of the prescribe time is transformed into the conventional system convergence problem. The improved Lyapunov function, the improved tuning function, and the adaptive fault-tolerant mechanism are further constructed. Combined with the neural network, the prescribe time tracking control of the speed subsystem and the height subsystem are realized respectively. Combined with the Barbalat lemma and Lyapunov stability theory, the boundedness of the closed-loop system is proved. The simulation results have proven that, compared with other control strategies, it can ensure that the tracking error converges to the prescribe interval in the prescribe time and meets the constraints of the whole state of the system.

Accuracy of electro-mechanical actuator in aircraft is susceptible to variable operation conditions such as electromagnetic interference, changeable temperature or loss of maintenance, leading in turn to flight performance degradation. This paper proposed an unified control paradigm that aims to keep aircraft’s velocity in a safe boundary and shorten the system stabilizing time in presence of actuator deviation. The controller is derived following a practical finite-time-convergence (FTC) with extended dynamics, and an integrated state-constraint structure so as to restrict air vehicle’s attitude rate or translation velocity. It is proved that the system state converges to a sphere near the origin in a finite time, the state trajectory is always remain within the prescribed range, and all signals of the closed-loop system are uniformly ultimately bounded. Compared simulation with the quadratic Lyapunov-based FTC method and an asymptotic convergence controller are conducted on an unmanned helicopter prototype. Results show that the proposed controller enhances the dynamic and fault-tolerant performance of resisting actuator fluctuation.

Abstract This paper proposes an adaptive fault‐tolerant control (FTC) method for hypersonic vehicle (HSV) with unexpected centroid shift, actuator fault, time‐varying full state constraints, and input saturation. The occurrence of unexpected centroid shift has three main effects on the HSV system, which are system uncertainties, eccentric moments, and variation of input matrix. In order to ensure the time‐varying state constraints, a novel attitude state constraint control strategy, to keep the safe flight of HSV, is technically proposed by a time‐varying state constraint function (TVSCF). A unified controller is designed to handle the time‐varying state constraints according to the proposed TVSCF. Then, the constrained HSV system can be transformed into a novel free‐constrained system based on the TVSCF. For the variation of system input matrix, input saturation and actuator fault, a special Nussbaum‐type function is designed to compensate for those time‐varying nonlinear terms. Additionally, the auxiliary systems is designed to compensate the constraint of system control inputs. Then, it is proved that the proposed control scheme can guarantee the boundedness of all closed‐loop signals based on the Lyapunov stability theory. At last, the simulation results are provided to demonstrate the effectiveness of the proposed fault‐tolerant control scheme.

Nonlinear controls that account for constraints on the state variable of overhead cranes can hardly strengthen the effective coupling between trolley movement and load oscillation, thus possessing little capacity in oscillation suppression. Nevertheless, such control designs trend to be more complex under parametric uncertainties. To solve these problems, this paper employs novel barrier functions in the coupling control design, so that the obtained feedback can preserve all states, including the composite variable, bounded within asymmetric limits while simultaneously enhancing antisway effectiveness. Owing to the simple structure of the Lyapunov derivative, the adaptation facilitates the proposed controller with robustness to parametric uncertainties. LaSalle's invariance principle ensures the asymptotic stability, and experiments verify the validity of the suggested controller. [ABSTRACT FROM AUTHOR]

This article investigates the issue of adaptive neural optimal fault‐tolerant control for a class of nonlinear uncertain systems subject to dynamic state constraints and external disturbances. To handle more general dynamic constraints, a unified tangent‐type nonlinear mapping is first proposed to transform the state‐constrained system into one free of constraints. To solve the problem of actuator faults and external disturbances, a single network adaptive dynamic program method is designed, which consists of a feed‐forward fault‐tolerant control scheme and a feedback differential game control strategy. Neural networks are employed to approximate the uncertainties and cost function, respectively. To handle the issue of "explosion of complexity," a finite‐time convergent differentiator is established to estimate the derivative of virtual control signals in the backstepping design. Via Lyapunov stability analysis, asymptotic stability of the original and transformed nonlinear system is theoretically guaranteed. Two comparative simulation examples are provided to evaluate the efficacy of the proposed control approach. [ABSTRACT FROM AUTHOR]

A supremum-of-quadratics representation for a class of extended real valued barrier functions is developed and applied in the context of solving a continuous time linear regulator problem subject to a single state constraint of bounded norm. It is shown that this very simple state constrained regulator problem can be equivalently formulated as an unconstrained two-player game. By demonstrating equivalence of the upper and lower values, and exploiting existence and uniqueness of the optimal actions for both players, state feedback characterizations for the corresponding optimal policies for both players are developed. These characterizations are illustrated by a simple example. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive fault‐tolerant control (FTC) method for hypersonic vehicle (HSV) with unexpected centroid shift, actuator fault, time‐varying full state constraints, and input saturation. The occurrence of unexpected centroid shift has three main effects on the HSV system, which are system uncertainties, eccentric moments, and variation of input matrix. In order to ensure the time‐varying state constraints, a novel attitude state constraint control strategy, to keep the safe flight of HSV, is technically proposed by a time‐varying state constraint function (TVSCF). A unified controller is designed to handle the time‐varying state constraints according to the proposed TVSCF. Then, the constrained HSV system can be transformed into a novel free‐constrained system based on the TVSCF. For the variation of system input matrix, input saturation and actuator fault, a special Nussbaum‐type function is designed to compensate for those time‐varying nonlinear terms. Additionally, the auxiliary systems is designed to compensate the constraint of system control inputs. Then, it is proved that the proposed control scheme can guarantee the boundedness of all closed‐loop signals based on the Lyapunov stability theory. At last, the simulation results are provided to demonstrate the effectiveness of the proposed fault‐tolerant control scheme. [ABSTRACT FROM AUTHOR]

This article is committed to studying the tracking control problem for a class of uncertain nonlinear system with unknown control coefficients. The system is subject to full-state constraints, input saturation constraint, and external disturbances simultaneously. By introducing a hyperbolic tangent function to approximate the saturated input function, the sharp corner caused by the input saturation is avoided. In the meanwhile, an auxiliary system is constructed to compensate the approximation error. By using the barrier Lyapunov function based adaptive backstepping control, the Nussbaum-type adaptive controllers are constructed for the augmented system with unknown control direction. It not only ensures the system states are always within the constrained range, but also guarantees the tracking performance of the system, no matter whether the control direction of the system is known or not. Meanwhile, dynamic surface control is used in the controller design, which avoids 'computation explosion' caused by the repeated derivation of virtual control law. It improves the tracking performance of the system and reduces the burden of the controller greatly. Finally, a simulation example is given to demonstrate the effectiveness of the proposed control scheme in three scenarios. [ABSTRACT FROM AUTHOR]

Summary: In this paper, the adaptive fault‐tolerant control (FTC) problem of heterogeneous multi‐agent systems (HMASs) with state constraints composed of first‐order and second‐order agents is studied. The problems of fault and constraints are inevitable during the operation of the system, the authors consider the fault of the system as actuator fault, and the constraints of the system can be considered as state constraints. Based on the backstepping framework, the logarithmic barrier Lyapunov function is selected to study the stability of system with constraints. For the bias fault of actuator fault, adaptive estimation is carried out, which can estimate the fault more accurately. Finally, an adaptive constrained FTC scheme is successfully designed to ensure that each signal of the system is bounded. Simulation examples show that the constrained FTC scheme is effective. [ABSTRACT FROM AUTHOR]

An optimal control problem is considered in which the integral term of the functional to be minimized contains the characteristic function of a given open set of undesirable system states. The statement of this problem can be viewed as a weakening of the statement of the standard optimal control problem with a state constraint. Conditions are obtained that guarantee the equivalence of these problems. Two illustrative examples are given. [ABSTRACT FROM AUTHOR]

Most existing solutions that guarantee finite-time convergence of a constrained first-order sliding mode either assume that the structure of the perturbation is known apriori, or the perturbation and its derivative are bounded by unknown constants. Moreover, convergence is usually guaranteed only in a small domain of attraction of the predefined constrained region through discontinuous control action. In contrast with these approaches, the sliding mode is assumed to be subject to perturbations with a state-dependent structure in this study, and two adaptive integral control strategies are proposed that guarantee finite-time convergence of this perturbed sliding mode from any initial condition within the predefined constrained region. First, an invertible nonlinear map is used to transform the constrained system into a constraint-free system, and an adaptive integral control strategy is used to guarantee finite-time convergence of the resulting sliding mode to a uniform ultimate bound using continuous and bounded control action. Subsequently, an alternative barrier-function based adaptive control policy is synthesized that ensures sliding mode convergence in a prescribed time to a prescribed bound that is independent of the magnitude of the perturbation term. Experimental studies of vision-based leader-follower formation control are used to validate and demonstrate superior performance of the proposed schemes compared to leading alternative designs.

We consider the basic problem of the Calculus of variations of minimizing an integral functional among the absolutely continuous functions that satisfy prescribed boundary conditions. We resume the state of the art and our recent contributions concerning the validity of the Du Bois-Reymond condition, and the Lipschitz regularity of the minimizers and of minimizing sequences (e.g., Lavrentiev phenomenon).

Copyright of Systems Engineering & Electronics is the property of Journal of Systems Engineering & Electronics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The problem of controlling fractional-order nonlinear systems remains interesting and challenging due to the powerful and hereditary memory features of such systems. In this paper, we investigate the adaptive tracking control problem for a class of fractional-order nonlinear systems with or without state constraints. The tan-type barrier Lyapunov function (BLF) is adopted for the first time in fractional Lyapunov direct method. Such technique allows for the accommodation of the situations with and without state constraints in a unified framework. Moreover, neural network (NN) is utilized to reconstruct the sophisticated nonlinear functions arising from the fractional-order differentiation of the virtual controller, resulting in a neuroadaptive fault-tolerant control scheme. It is shown that, with the proposed unified control, all the closed-loop signals are semiglobally ultimately uniformly bounded whether state constraints are imposed or not. Both theoretical analysis and numerical simulation confirm the effectiveness of the developed approach. [ABSTRACT FROM AUTHOR]

Copyright of Systems Engineering & Electronics is the property of Journal of Systems Engineering & Electronics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper is devoted to second-order necessary optimality conditions for a class of infinite-dimensional optimal control problems under functional pure state constraints together with end point constraints. Using tools of second-order variational analysis, we derive necessary optimality conditions in the form of a minimum principle and a second-order variational inequality. We further propose sufficient conditions guaranteeing normality of the minimum principle. Finally, applications to optimal control models involving PDEs are provided. [ABSTRACT FROM AUTHOR]

In this article, we propose a new iterative learning control (ILC) scheme for trajectory tracking of pneumatic muscle (PM) actuators with state constraints. A PM model is constructed in three-element form with both parametric and nonparametric uncertainties, while full state constraints are considered for enhancing operational safety. To ensure that system states are within the predefined bounds, the barrier Lyapunov function (BLF) is used in the analysis, which reaches infinity when some of its arguments approach limits. The proposed ILC incorporates the BLF with the composite energy function (CEF) approach and ensures the boundedness of CEF in the closed-loop, thus, assuring that those limits are not transgressed. Through rigorous analysis, we show that under the proposed ILC scheme, uniform convergences of PM state tracking errors are guaranteed. Simulation studies and experimental validations are conducted to illustrate the efficacy of the proposed scheme. Experimental results show that the proposed ILC satisfies the state constraint requirements and the tracking error is less than 2.5% of the desired trajectory. [ABSTRACT FROM AUTHOR]

We consider the spectral approximation of flow optimal control problems with state constraint. The main contribution of this work is to derive an a posteriori error estimator, and show the upper and lower bounds for the approximation error. Numerical experiment shows the efficiency of the error indicator, which will be used to construct reliable adaptive hp spectral element approximation for flow control in the future work.

It is still an open problem to achieve tracking control with state constraints if the initial states are out of the constrained region. This underlying problem becomes more challenging if the system suffers from modeling uncertainties and external disturbances. In this paper, we investigate such problem for a class of uncertain nonaffine self‐restructuring systems subject to state constraints in the absence of any limitation on the initial values of states. In order to steer the original system states into the desired constraint region in finite time, certain auxiliary system is firstly constructed via introducing auxiliary variables. By resorting to some auxiliary nonlinear functions, the original system with state constraints is transformed into an unconstrained one in the sense that the constraint problem of the original system is equivalent to ensuring the stability of the transformed one. By following the backstepping design technique, an adaptive control scheme is developed that enables the states to enter into the constrained region for any initial point within any fixed time and then never violate it. All the closed loop signals are ensured to be semi‐globally uniformly ultimately bounded. Finally, one numerical simulation example is presented to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

We consider a time-optimal problem for the classical "double integrator" system under an arbitrary linear state constraint. Using the maximum principle, we construct the full synthesis of optimal trajectories and provide a qualitative investigation of the measure, the Lagrange multiplier corresponding to the state constraint. [ABSTRACT FROM AUTHOR]

In this paper, the state-constrained adaptive control problem for a class of uncertain fractional-order nonlinear systems with unknown external disturbances is studied. Using the fuzzy approximation and backstepping control layout, an adaptive disturbance-observer-based control method is proposed, which can effectively estimate the unknown external disturbances through the designed disturbance observers. As we know, the standard backstepping control has inherent computational complexity. Therefore, a design approach of fractional-order command filter is introduced, which takes advantage of fractional-order command filter to pre-estimate the virtual input signal and its fractional derivative. In addition, barrier Lyapunov functions are exploited to cope with the fractional states-constrained control problem. The combination of barrier Lyapunov function technique and backstepping design not only ensures excellent tracking performance, but also enhances the robustness of the system. Furthermore, based on the fractional Lyapunov approach, the relevant stability analysis is established, which demonstrates that all states of the system remain within their constrained scope, and all signals of the closed-loop system are bounded. Finally, the effectiveness of the proposed scheme is verified by numerical simulation examples of RLC circuit and horizontal platform system. [ABSTRACT FROM AUTHOR]

This work focuses on optimal harvesting-renewing for a stochastic population. A mixed regular-singular control formulation with a state constraint and regime switching is introduced. The decision-makers either harvest or renew with finite or infinite harvesting/renewing rates. The payoff functions depend on the harvesting/renewing rates. Several properties of the value function are established. The limiting value function as the white noise intensity approaches infinity is identified. The Markov chain approximation method is used to find numerical approximation of the value function and optimal strategies. [ABSTRACT FROM AUTHOR]

We revisit the optimal control problem with maximum cost with the objective to provide different equivalent reformulations suitable to numerical methods. We propose two reformulations in terms of extended Mayer problems with state constraints, and another one in terms of a differential inclusion with upper-semi-continuous right member without state constraint. For the latter we also propose a scheme that approximates from below the optimal value. These approaches are illustrated and discussed in several examples. [ABSTRACT FROM AUTHOR]

We consider the spectral approximation of flow optimal control problems with state constraint. The main contribution of this work is to derive an a posteriori error estimator, and show the upper and lower bounds for the approximation error. Numerical experiment shows the efficiency of the error indicator, which will be used to construct reliable adaptive hp spectral element approximation for flow control in the future work. [ABSTRACT FROM AUTHOR]

Considering the lumped disturbances and initial conditions limit for prescribed performance, this paper addresses a state-constrained safety trajectory tracking control scheme for a hovercraft. Firstly, model of hovercraft will be introduced. Then, adaptive prescribed-time extended state observer (APESO) is proposed to handle lumped disturbances. Secondly, considering position errors with prescribed performance relying on the initial conditions, for the sake of eliminating the dependence, a composite error transformation technique based on a continuously differentiable time-varying function is introduced. Initial errors of the hovercraft position can be compressed to a definable range. Then, virtual velocity control laws are obtained by a prescribed performance function (PPF) combined with a sliding mode. Thirdly, in order to solve problems of velocity safety constraints, an improved unified barrier function (IUBF) is introduced to limit hovercraft velocities within the asymmetric safety constraints. In addition, combined with auxiliary systems, a command filter will be introduced to reduce complex derivative calculation burden in hovercraft system controller design and avoid the phenomenon of "differential explosion". Total system states are ultimately uniformly bounded according to stability theories for cascade system. Finally, simulations illustrate the effectiveness of the proposed controller of the hovercraft. • By comparison with existing researches, aim to eliminate the dependence, a composite error transformation technique based on a continuously differentiable time-varying function is introduced. Initial position errors can be compressed to a definable set. Aim to avoid sudden compression to zero regardless of the actual value, the proposed function maximizes the initial error's original information and gently compresses it. Ignoring initial condition of position in PPC expands the application scenarios of trajectory tracking tasks for hovercraft. • Considering state constraints, aim to ensure velocities be restrained into asymmetric boundaries, a new safety controller based on IUBF is designed. Compared with previous works [62–65], the presented controller can eliminate the feasibility condition. On the other hand, compared with (Zheng et al., 2023; Wang et al., 2024c), the IUBF can be adopted to handle the systems with and without constraint concurrently and uniformly. Therefore, it is convenient for drivers to operate and expands the application scenarios of trajectory tracking tasks for hovercraft. • Aim to estimate lumped disturbances with good performance, an APESO is presented for a hovercraft. No matter what initial conditions mentioned, a design parameter can strictly prescribe the upper bound of settlement time. Compared with aforementioned finite-time ESOs (FTESOs) (Gu et al., 2019; Liu et al., 2020; Wang et al., 2021b; Yu et al., 2021) and fixed-time ESOs (FXESOs) (Zhang et al., 2019, 2020; Gu et al., 2021; Wang et al., 2022), the proposed observer has more superior. [ABSTRACT FROM AUTHOR]

This paper addresses the event-triggered stabilization problem for nonlinear control-affine systems under state constraints. First, a strong control Lyapunov barrier function (CLBF) method is applied for constructing continuous state-constrained stabilizing controllers. Additionally, sufficient conditions for the existence of strong CLBFs are derived. With the obtained state-constrained feedback laws, a new event-triggered policy is proposed for reducing the number of communication events without the input-to-state stability (ISS) assumption. It is proved that the Zeno behavior is excluded under this event-triggered policy, that is, the inter-execution times are lower bounded away from zero. Finally, two examples are included to illustrate the theoretical results.

In this paper, the finite-time constrained set stabilisation of delayed probabilistic Boolean control networks (DPBCNs) is considered via sampled-data control (SDC). The main mathematical tool is semi-tensor product of matrices, which is used to convert the dynamics of DPBCNs into an equivalent algebraic state space representation (ASSR). Based on the ASSR of DPBCNs, the constrained sampled-data transition probability matrix is constructed. Then, new criteria are proposed for the finite-time constrained reachability of DPBCNs under uniform SDC. By virtue of finite-time constrained reachability, a procedure is established to design state feedback sampled-data stabilisers for DPBCNs. The obtained results are applied to the 'minimal' model of lactose operon in E. coli. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of formation fault-tolerant control of multiple quadrotors (QRs) for a mobile sensing oriented application. The QRs subject to faults, input saturation and time-varying delays can be controlled to perform a target-enclosing and covering task while guaranteeing the state constraints will not be exceeded. A distributed formation control scheme is proposed, using a radial basis function neural network (RBFNN)-based time-delay position controller and an adaptive fault-tolerant attitude controller. The Lyapunov–Krasovskii approach is used to analyze the time-varying delay. Barrier Lyapunov function is deployed to handle the prescribed constraints, and an auxiliary system combined with a command filter is designed to resolve the saturation problem. An RBFNN and adaptive estimators are deployed to provide estimates of disturbances, fault signals and uncertainties. It is proven that all the closed-loop signals are bounded under the proposed protocol, while the prescribed constraints will not be violated, which enhances the flight safety and QR formation's applicability. Comparative simulations based on application scenarios further verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Employing a continuous-time control algorithm to control the practical system based on discrete-time digital computer will lead to the cost of performance degeneration. To address this issue, this paper proposes a discrete-time barrier Lyapunov function based controller for human–robot interaction in constrained task space to guarantee control performance. The Euler discrete-time stability of closed-loop system controlled by the proposed method is proved, and a feasible difference scheme to support the stability analysis is uncovered based on monotonic scaling. The parameter dependence of this study is well discussed, which involves sample interval and preset boundary of state constraints, and based on the architecture of barrier Lyapunov function, the dependence relationship is demonstrated by using analytical synthesis technique. With a certain sample interval, the proposal of controller parameters is qualified to guarantee that end-effector states are constrained with preset boundary. The discrete-time neural network estimation is designed to approximate the human being's behavior to rebuild the reference trajectory from the desired trajectory and impedance for smoothing the human–robot interaction. Controlled discrete-time states and estimated force are uniformly ultimately bounded, and the convergence vicinity around the origin is proven to be determined by sample interval, lumped uncertainty and preset boundary of state constraints. Numerical simulation and experimental results verify the effectiveness of proposed discrete-time barrier Lyapunov function based methods. • The proposed controller is capable of guaranteeing that the discrete-time constrained states are uniformly ultimately bounded. • The tolerance of error between the state and the boundary is expressed quantitatively. • The operation behavior is estimated by the one-step discrete-time NN technique. • The superior performance of the proposed method is confirmed by experimental results. [ABSTRACT FROM AUTHOR]