Acceleration Saturation Research Articles

Nonlinear effects of saturation in the car-following model

The goal of this paper is to provide insight about the effect of acceleration saturation in the car-following model. In this contribution, we consider a heterogeneous, mixed-traffic scenario which contains both human-driven and autonomous vehicles subjected to time delays. Corresponding stability charts are provided from which one can tune the control parameters of the automated vehicles to achieve smooth traffic flow. By taking into account the acceleration saturation, it modifies the global behaviour of the system and reduces the range of the optimal technological parameters. On a demonstrative example, we highlight the complex dynamical phenomenon induced by the saturation and we attempt to connect these nonlinear investigations to the engineering practice and point out their relevance.

Terminal angle constraint finite-time guidance law with input saturation and autopilot dynamics

This paper proposes a finite-time command filtered backstepping guidance law (FCFBGL) with the terminal angle constraint while accounting for the input saturation and the autopilot dynamics. To eliminate the adverse effect induced by the filtering errors and the acceleration saturation, a new finite-time error compensation mechanism is integrated in the guidance law design. The proposed FCFBGL not only guarantees the the line-of-sight (LOS) angle error to converge to a small neighborhood of the origin in finite time but also achieves the continuity of the input signal. in finite time. Moreover, with the aid of the fractional power extended state observer (FPESO), the proposed FCFBGL requires no information on the target acceleration and the acceleration derivative of the missile, which is preferable in the practical application. The finite-time stability of the proposed guidance law is derived with the Lyapunov methodology. Simulation results illustrate the effectiveness and superiority of the proposed guidance law.

Adaptive Fast Fixed-Time Three-Dimensional Guidance Law With Acceleration Saturation Constraints

This paper investigates continuous anti-saturation three-dimensional guidance law against maneuvering target at the desired line-of-sight (LOS) angles. Firstly, in the light of fixed-time stability, fast nonsingular terminal sliding mode is designed without the limitation of odd-ratio fractional order. Then, with the limits of lateral acceleration saturation, continuous guidance law is proposed to guarantee that desired LOS angles are reached and maintained after the specified time, while adaptive law is implemented to estimate the information on maneuver accelerations of the attacking missile. Finally, numerical simulations are presented to validate the effectiveness and rationality of the designed scheme.

Novel command to line of sight guidance with practical limitations

AbstractIn this paper, a novel scheme of command to line‐of‐sight guidance law regarding the outstanding practical limitations is proposed. With the aid of formulating problem in pursuer's line of sight frame, the exact feed‐forward acceleration commands are derived for a general target motion in three‐dimensional engagement geometry. Then, a nonlinear control scheme constructed from feed‐forward terms along with a nested saturated feedback strategy is suggested. Two momentous practical limitations are considered. The first is related to existence of pursuer's acceleration saturation which is ignored in all existing solutions. The required conditions to insure the global stability are derived regarding this inevitable constraint. The second is related to existence of guidance filter which is assumed to be ideal in existing literature. The importance of guidance filter is highlighted in the present work employing a cubature Kalman filter. The effectiveness of proposed scheme in comparison with the well‐known augmented proportional navigation law, with the absence and presence of guidance filter, autopilot dynamics and target maneuvers is illustrated through benchmark scenarios.

Visual tracking of mobile robots with both velocity and acceleration saturation constraints

In this paper, an adaptive visual tracking controller is proposed for the nonholonomic mobile robot with an onboard monocular camera, wherein both the velocity and acceleration saturation constraints can be guaranteed by properly selecting the control parameters during the visual servoing process. Specifically, the virtual velocity-level controller is firstly designed based on the first-order filter, by which the bounds of the virtual velocity signals can be estimated. Then, according to the finite-time control theory, the actual acceleration-level controller is developed to track the virtual velocity input in a finite time. For the unknown distance between the plane of feature points and the origin of the global frame due to the lack of the image depth, an adaptive updating law is designed and also used for the parameter identification. The global asymptotical stability of the closed-loop system is proven using Lyapunov techniques with Barbalat’s lemma. The calculations for the upper bounds of velocity and acceleration signals are given. In addition, some tips for the control gains tuning in practical experiments are summarized. Experimental results are provided to validate the effectiveness of the proposed controller.

Auxiliary-system-based composite adaptive optimal backstepping control for uncertain nonlinear guidance systems with input constraints

This paper addresses a missile–target interception guidance process considering acceleration saturation and target maneuver as a constrained nonlinear tracking issue. A dynamic auxiliary system is designed for compensating the effects of constrained input, and external disturbances are counteracted through designing a nonlinear disturbance observer (NDO). The feedforward+feedback composite architecture is built in which a feedforward backstepping control and a feedback optimal control is presented recurrently. Furthermore, the parameter adaptive updating laws are derived to estimate the unknown functions online. Subsequently, the boundedness of the closed-loop signals are guaranteed. The predefined cost function is also ensured to be minimized. Furthermore, the control input is prevented violating its boundary. The contrastive simulation results demonstrate that the robustness of the proposed method is more superior to the nonsingular terminal sliding mode (NTSM) and the proportional navigation (PN) methods.

Cooperation of Multiple Connected Vehicles at Unsignalized Intersections: Distributed Observation, Optimization, and Control

Cooperation of connected vehicles is a promising approach for autonomous intersection control. This article presents a systematic approach to the cooperation of connected vehicles at unsignalized intersections without global coordination. A task-area partition framework is proposed to decompose the mission of cooperative passing into three main tasks, i.e., vehicle state observation, arriving time optimization, and trajectory tracking control. To accomplish these tasks, a distributed observation algorithm is introduced to achieve fixed-time observation of other vehicles’ states for passing sequence determination, a distributed optimization algorithm is introduced to schedule conflict-free arriving times for trajectory planning, and a distributed control algorithm is proposed to address parameter mismatches and acceleration saturation for fixed-time trajectory tracking control. Numerical simulations demonstrate that the proposed method can achieve cooperative passing of vehicles without global coordination at the cost of a growth of 8.8–18.1% average travel times in low and medium traffic volumes.

Design of Three-Dimensional Guidance Law With Impact Angle Constraints and Input Saturation

This thesis studies the problem of three-dimensional guidance considering maneuvering acceleration and input saturation based on the background of missile intercepting maneuvering target. On the basis of the three-dimensional guidance model with impact angle constraints, a three-dimensional guidance law is designed by using the integral sliding mode control and adaptive control. To solve the problem of input saturation, an adaptive anti-saturation integral sliding mode three-dimensional guidance law is designed by introducing an auxiliary system. The stability of the designed guidance law is proved by Lyapunov theory, which ensures that the sliding mode manifold converges to zero in finite time. The effectiveness of the designed guidance law is verified by simulation analysis.

Adaptive back-stepping sliding mode guidance laws with autopilot dynamics and acceleration saturation consideration

This paper studies the guidance scheme for the terminal guidance problem subject to input constraints, attack angle constraints, and second-order dynamics of missile autopilot. Firstly, the guidance system model with the above multi-constraint model is given. Secondly, an anti-saturation back-stepping guidance law which makes use of the low-pass filter to avoid the differential of the virtual control signals is designed based on the terminal sliding mode method, auxiliary system, and adaptive technique. Finally, Lyapunov theory and numerical simulations are utilized to prove that the states of the system under the proposed guidance law are uniformly ultimately bounded.

Distributed Control of Vehicle Strings Under Finite-Time and Safety Specifications

This paper studies an optimal control problem for a string of vehicles with safety requirements and finite-time specifications on the approach time to a target region. Our problem formulation is motivated by scenarios involving autonomous vehicles circulating on arterial roads with intelligent management at traffic intersections. We propose a provably correct distributed control algorithm that ensures that the vehicles satisfy the finite-time specifications under speed limits, acceleration saturation, and safety requirements. The safety specifications are such that collisions can be avoided even in cases of communication failure. We also discuss how the proposed distributed algorithm can be integrated with an intelligent intersection manager to provide information about the feasible approach times of the vehicle string and a guaranteed bound of its time of occupancy of the intersection. Our simulation study illustrates the algorithm and its properties regarding approach time, occupancy time, and fuel and time cost.

Robust impact angle constraints guidance law with autopilot lag and acceleration saturation consideration

In this paper, for the three-dimensional terminal guidance problem of a missile intercepting a manoeuvring target, a robust continuous guidance law with impact angle constraints in the presence of both an acceleration saturation constraint and a second-order-lag autopilot is developed. First, based on non-singular fast terminal sliding mode and adaptive control, a step-by-step backstepping method is used to design the guidance law. In the process of guidance law design, with the use of a finite-time control technique, virtual control laws are developed, a tracking differentiator is used to eliminate the ‘explosion of complexity’ problem inherent in the traditional backstepping method, and an additional system is constructed to deal with the acceleration saturation problem; its states are used for guidance law design and stability analysis. Moreover, the target acceleration is considered bounded disturbance, but the upper bound is not required to be known in advance, whereas the upper bound is estimated online by a designed adaptive law. Next, finite-time stability of the guidance system is strictly proved by using a Lyapunov method. Finally, numerical simulations are presented to demonstrate the excellent guidance performances of the proposed guidance law in terms of accuracy and efficiency.

Adaptive Fuzzy Sliding Mode Guidance Law considering Available Acceleration and Autopilot Dynamics

Terminal guidance law for missiles intercepting high maneuvering targets considering the limited available acceleration and autopilot dynamics of interceptor is investigated. Conventional guidance laws based on adaptive sliding mode control theory were designed to intercept a maneuvering target. However, they demand a large acceleration for interceptor at the end of the terminal guidance, which may have acceleration saturation especially when the target acceleration is close to the available acceleration of interceptor. In this paper, a terminal guidance law considering the available acceleration and autopilot dynamics of interceptor is proposed. Then, a fuzzy system is utilized to approximate and replace the variable structure term, which can handle the unknown target acceleration. And an adaptive neural network system is adopted to compensate the effects caused by the designed overlarge acceleration of interceptor such that the interceptor with small available acceleration can intercept the high maneuvering target. Simulation results show that the guidance law with available acceleration and autopilot dynamics (AAADG) is highly effective for reducing the acceleration command and achieving a small final miss distance.

Translational and Scaling Formation Maneuver Control via a Bearing-Based Approach

This paper studies distributed maneuver control of multi-agent formations in arbitrary dimensions. The objective is to control the translation and scale of the formation while maintaining the desired formation pattern. Unlike conventional approaches where the target formation is defined by relative positions or distances, we propose a novel bearing-based approach where the target formation is defined by inter-neighbor bearings. Since the bearings are invariant to the translation and scale of the formation, the bearing-based approach provides a simple solution to the problem of translational and scaling formation maneuver control. Linear formation control laws for double-integrator dynamics are proposed and the global formation stability is analyzed. This paper also studies bearing-based formation control in the presence of practical problems including input disturbances, acceleration saturation, and collision avoidance. The theoretical results are illustrated with numerical simulations.

Adaptive backstepping impact angle control with autopilot dynamics and acceleration saturation consideration

SummaryThis paper presents a robust impact angle constraint guidance law for maneuvering target interception in the presence of autopilot dynamics and input saturation. The presented guidance law is designed on the basis of a combination of adaptive backstepping control technique and higher‐order sliding mode differentiator. Different from existing impact angle constraint guidance law using sliding mode control, the line‐of‐sight angular rate and impact angle tracking error are regulated by two different virtual control laws. Because the future course of action of the target, an independent entity, cannot be predicted beforehand, adaptive laws are introduced in guidance law derivation for disturbance rejection. Unlike dynamic surface control approach, higher‐order sliding mode differentiator is adopted here as an alternative way to obtain the derivatives of the virtual control laws, thus leading to the exact tracking performance of backstepping control. Detailed stability analysis shows that both the line‐of‐sight angular rate and impact angle error can be stabilized in a small region around zero asymptotically. Simulation results explicitly show that accurate interception is achieved with a wide range of impact angles. Copyright © 2017 John Wiley & Sons, Ltd.

Finite time sliding sector guidance law with acceleration saturation constraint

A novel guidance law utilising variable structure control with finite time sliding sector is proposed. In contrast with the normally used notion of asymptotic stability in conventional sliding sector, a finite time sliding sector is defined as a subset of state space in which the Lyapunov function candidate satisfies the finite time stability condition. For the guidance system, the analytical solution of a state-dependent differential Riccati equation is achieved to determine the finite time sliding sector. Then, based on the finite time sliding sector, a sliding sector guidance law is designed by considering the target acceleration as a bounded uncertainty. Furthermore, the finite time sliding sector guidance law is even extended to the case where missile acceleration saturation constraint is considered. Simulation results show that the new guidance law is highly effective.

Closed-form optimal cooperative guidance law against random step maneuver

Based on the optimal control theory, the present study proposes a novel approach to derive a cooperative guidance law for two pursuers with an arbitrary-order linear dynamics against one zero-lag evader with random step maneuver. This approach is intended to minimize the mean value of the resultant control effort taken over a set of possible evader maneuvers which is modeled as a step function, the parameters of which are unknown. Since the resultant control effort is the minimum effort among the pursuers, we encounter the nonlinear “min” function in the performance index. By introducing binary parameters, it is changed to a linear function including binary parameters and continuous variables. After the optimal control problem is solved, the optimal binary parameters are determined through an integer programming approach. Then, the closed-form optimal cooperative guidance law (OCGL) is derived in feedback form. The analytical and numerical results, obtained for the engagement of two missiles against a maneuvering target, show that OCGL is superior to the noncooperative guidance laws such as proportional navigation (PN) and optimal guidance law (OGL), even if the real model, used in evaluations, differs from the model used in the derivation of the guidance law. The performance of the proposed guidance law has been evaluated for higher order dynamics at the presence of acceleration saturation.

Finite‐time cooperative guidance laws for multiple missiles with acceleration saturation constraints

The problem of cooperative guidance of multiple missiles attacking a stationary target, which can be achieved by consensus of the times-to-go is illustrated in this study. First, the finite-time cooperative guidance (FTCG) law is put forwarded to realise rapid and precise consensus of the times-to-go of all the missiles. Then, the FTCG law is modified to accommodate the condition in the presence of acceleration saturation constraint, and global ultimately finite-time consensus of times-to-go is also guaranteed. Finally, in order to adapt the realistic situation that each missile can only employ neighbour-to-neighbour communication, the distributed FTCG law is proposed. This guidance law adopts the sequential method, and can also cope with acceleration saturation constraint. The simulation results based on current control scheme and the comparison with the previous method demonstrate the effectiveness of the proposed laws.

Optimal Linear-Quadratic Missile Guidance Laws with Penalty on Command Variability

This paper proposes a new approach to the derivation of homing guidance laws for interceptor missiles that makes use of linear-quadratic optimal control in a different manner than the traditional approaches. Instead of looking only for the minimization of the miss distance and the integral square of the guidance command, the new criterion penalizes also the “variability” of the guidance command. The solution has the familiar structure of traditional linear-quadratic guidance laws, of a zero-effort-miss term multiplied by a, possibly time-varying, gain. Still it differs in one essential feature: The navigation gain does not only depend on the time to go, but also on the total time of flight. The new guidance law also has an additional design parameter that can be profitably used to avoid acceleration saturation.

Target Maneuver Adaptive Guidance Law for a Bounded Acceleration Missile

A new estimator-guidance law is presented, for a bounded acceleration interceptor pursuing a target performing a sudden step maneuver. The linearized end-game scenario is investigated. The missile’s acceleration saturation is represented by the equivalent random input describing function. The estimator proposed for this problem features a mechanism constructed to e‐ciently identify a sudden target maneuver. Due to the bound on the missile acceleration, the certainty equivalence property is not valid, and so, the resulting controller (guidance law) depends on the measurement noise level, statistics of the target maneuver, and the saturation limit. The derivation of this guidance law proceeds in two stages. In the flrst simplifled stage, it is assumed that the instance that the target issues a step command in its acceleration is known. However, the size of the target maneuver jump must still be estimated. Simulation results show signiflcant improvement over the deterministic optimal guidance law when the jump times vary from 10 to 3 missile time constants prior to the intercept time. If the jump occurs earlier or later than this duration no improvement is gained. In the second stage, a suboptimal guidance law is derived using the multiple model adaptive control formulation for a target performing a single step maneuver near the intercept time. Note that this sub-optimal guidance law does not require a-priory knowledge of the time of the jump in the target acceleration command. Performance improvement of the same order of magnitude as was observed for the known jump time scheme (that also serves as a performance bound) is achieved, verifying the validity of this approach. Sensitivity analysis to various noise levels and expected target maneuvers was carried out emphasizing the robustness and advantages of this scheme.

LQC guidance law with bounded acceleration command

A novel missile guidance law that is dependent on the conditional probability density function of the estimated states is presented. The guidance law is derived by analyzing an interception scenario in the framework of an linear quadratic Gaussian (LQG) terminal control problem with bounded acceleration command. The nonlinear saturation function is represented by the equivalent random input describing function. Since for the investigated problem the certainty equivalence property is not valid, the resulting controller depends on the measurement noise level and on the saturation limit. In comparison to the classical optimal guidance law (OGL), the maximal value of the effective navigation gain is achieved during the engagement instead of near the terminal time. Thus, the saturation limit is reached earlier so as to have enough time to reduce the guidance errors. Using Monte-Carlo simulations, the superiority of the new guidance law over the classical OGL is shown. This validates the new approach of designing an estimation statistics dependent guidance law by using a random input describing function to approximate the missile's acceleration saturation.