Stabilization of Traffic Flow With a Leading Autonomous Vehicle

2018 ◽  
Author(s):  
Huan Yu ◽  
Shumon Koga ◽  
Miroslav Krstic
Keyword(s):  
Moving Boundary ◽  
Autonomous Vehicle ◽  
Loop System ◽  
Traffic Density ◽  
Control Law ◽  
State Variables ◽  
State Dependent ◽  
L2 Norm ◽  
Uniform Equilibrium ◽  
Domain Length

This paper develops boundary control law for autonomous vehicles to stabilize the stop-and-go traffic on freeway. The macroscopic traffic dynamics is described by the Aw-Rascle-Zhang (ARZ) model in a time and state dependent domain. The leading autonomous vehicle aims to regulate the traffic behind it to uniform equilibrium and the domain length of the traffic to a setpoint. The traffic density and speed is governed by second-order, nonlinear hyperbolic partial differential equations (PDEs), coupled with a state-dependent ODE for the leading autonomous vehicle. The actuation is the speed of autonomous vehicle at the moving front boundary of the domain. We linearize the system around a uniform velocity and density reference and certain physical properties are discussed for the model validity. The linearized model describes the dynamics of deviations of density and velocity from the reference. By transforming the linearized system in a moving coordinate, we obtain a domain with a fixed boundary at one end and a state-dependent moving boundary at the other end. The well-posedness of the system is proved and the linear instability of open-loop system is shown. We further map the system to Riemann variables and based on it, propose the boundary feedback control law actuated by the leading autonomous vehicle. The exponential stability of state variables in L2 norm and convergence to the setpoint domain length is achieved for the closed-loop system.

scholarly journals A Robust Observer—Based Adaptive Control of Second—Order Systems with Input Saturation via Dead-Zone Lyapunov Functions

Computation ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 82
Author(s):  
Alejandro Rincón ◽  
Gloria M. Restrepo ◽  
Fredy E. Hoyos
Keyword(s):  
Lyapunov Functions ◽  
Dead Zone ◽  
Tracking Error ◽  
Input Saturation ◽  
Chemical Reactor ◽  
Second Order ◽  
Control Law ◽  
Compact Set ◽  
State Variables ◽  
Robust Observer

In this study, a novel robust observer-based adaptive controller was formulated for systems represented by second-order input–output dynamics with unknown second state, and it was applied to concentration tracking in a chemical reactor. By using dead-zone Lyapunov functions and adaptive backstepping method, an improved control law was derived, exhibiting faster response to changes in the output tracking error while avoiding input chattering and providing robustness to uncertain model terms. Moreover, a state observer was formulated for estimating the unknown state. The main contributions with respect to closely related designs are (i) the control law, the update law and the observer equations involve no discontinuous signals; (ii) it is guaranteed that the developed controller leads to the convergence of the tracking error to a compact set whose width is user-defined, and it does not depend on upper bounds of model terms, state variables or disturbances; and (iii) the control law exhibits a fast response to changes in the tracking error, whereas the control effort can be reduced through the controller parameters. Finally, the effectiveness of the developed controller is illustrated by the simulation of concentration tracking in a stirred chemical reactor.

scholarly journals Suboptimal Regulation of a Class of Bilinear Interconnected Systems with Finite-Time Sliding Planning Horizons

2008 ◽  
Vol 2008 ◽  
pp. 1-26 ◽  
Author(s):  
M. de la Sen ◽  
Aitor J. Garrido ◽  
J. C. Soto ◽  
O. Barambones ◽  
I. Garrido
Keyword(s):  
Control Law ◽  
State Variables ◽  
Linear Quadratic ◽  
Equivalent Representation ◽  
Quadratic Performance Index ◽  
Matrix Sequence ◽  
Control Scheme ◽  
Quadratic Performance ◽  
System Equations ◽  
Riccati Matrix

This paper focuses on the suboptimization of a class of multivariable discrete-time bilinear systems consisting of interconnected bilinear subsystems with respect to a linear quadratic optimal regulation criterion which involves the use of state weighting terms only. Conditions which ensure the controllability of the overall system are given as a previous requirement for optimization. Three transformations of variables are made on the system equations in order to implement the scheme on an equivalent linear system. This leads to an equivalent representation of the used quadratic performance index that involves the appearance of quadratic weighting terms related to both transformed input and state variables. In this way, a Riccati-matrix sequence, allowing the synthesis of a standard feedback control law, is obtained. Finally, the proposed control scheme is tested on realistic examples.

scholarly journals Stochastic Game Theoretic Formulation for a Multi-Period DC Pension Plan with State-Dependent Risk Aversion

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 108 ◽  
Author(s):  
Liyuan Wang ◽  
Zhiping Chen
Keyword(s):  
Risk Aversion ◽  
Stochastic Game ◽  
Pension Plan ◽  
Time Inconsistency ◽  
State Variables ◽  
Economic Point ◽  
State Dependent ◽  
Equilibrium Control ◽  
Special Cases ◽  
Game Theoretic

When facing a multi-period defined contribution (DC) pension plan investment problem during the accumulation phase, the risk aversion attitude of a mean-variance investor may depend on state variables. In this paper, we propose a state-dependent risk aversion model which is a linear function of the current wealth level after contribution. This risk aversion model is reasonable from both the dimensional analysis and the economic point of view. Moreover, we incorporate the wage income factor into our model. In the field of dynamic investment analysis, most studies have irrational situations in their models because of the lack of the positiveness for the wealth process. In view of it, we further improve the work of Wang and Chen by completely eliminating the irrationality of the model. Due to the time-inconsistency of the resulting stochastic control problem, we derive the explicit expressions of the equilibrium control and the corresponding equilibrium value function by adopting the game theoretic framework developed in Björk and Murgoci. Further, two special cases are discussed. Finally, using a more realistic risk aversion coefficient, we provide a series of empirical tests based on the real data from the American market and compare our results with the relevant results in the literature.

scholarly journals Quantized-Feedback-Based Adaptive Event-Triggered Control of a Class of Uncertain Nonlinear Systems

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1603
Author(s):  
Yun Ho Choi ◽  
Sung Jin Yoo
Keyword(s):  
Nonlinear Systems ◽  
Total Sample ◽  
Control Law ◽  
Continuous Control ◽  
State Variables ◽  
Event Time ◽  
Quantized Feedback ◽  
Event Triggering ◽  
Sample Data ◽  
Event Triggered

A quantized-feedback-based adaptive event-triggered tracking problem is investigated for strict-feedback nonlinear systems with unknown nonlinearities and external disturbances. All state variables are quantized through a uniform quantizer and the quantized states are only measurable for the control design. An approximation-based adaptive event-triggered control strategy using quantized states is presented. Compared with the existing recursive quantized feedback control results, the primary contributions of the proposed strategy are (1) to derive a quantized-states-based function approximation mechanism for compensating for unknown and unmatched nonlinearities and (2) to design a quantized-states-based event triggering law for the intermittent update of the control signal. A Lyapunov-based stability analysis is provided to conclude that closed-loop signals are uniformly ultimately bounded and there exists a minimum inter-event time for excluding Zeno behavior. In simulation results, it is shown that the proposed quantized-feedback-based event-triggered control law can be implemented with less than 10% of the total sample data of the existing quantized-feedback continuous control law.

scholarly journals Multilevel Service-Provisioning-Based Autonomous Vehicle Applications

2020 ◽  
Vol 12 (6) ◽  
pp. 2497 ◽  
Author(s):  
Mashael Khayyat ◽  
Abdullah Alshahrani ◽  
Soltan Alharbi ◽  
Ibrahim Elgendy ◽  
Alexander Paramonov ◽  
...  
Keyword(s):  
Communication Networks ◽  
Autonomous Vehicles ◽  
Autonomous Vehicle ◽  
Access Network ◽  
High Mobility ◽  
Base Stations ◽  
Traffic Density ◽  
Fifth Generation ◽  
Radio Access ◽  
Vehicle Networks

With the recent advances and development of autonomous control systems of cars, the design and development of reliable infrastructure and communication networks become a necessity. The recent release of the fifth-generation cellular system (5G) promises to provide a step towards reliability or a panacea. However, designing autonomous vehicle networks has more requirements due to the high mobility and traffic density of such networks and the latency and reliability requirements of applications run over such networks. To this end, we proposed a multilevel cloud system for autonomous vehicles which was built over the Tactile Internet. In addition, base stations at the edge of the radio-access network (RAN) with different technologies of antennas are used in our system. Finally, simulation results show that the proposed system with multilevel clouding can significantly reduce the round-trip latency and the network congestion. In addition, our system can be adapted in the mobility scenario.

Application of optimal control law to laser guided bomb

2018 ◽  
Vol 122 (1251) ◽  
pp. 785-797
Author(s):  
Takieddine Mouada ◽  
Milos V. Pavic ◽  
Bojan M. Pavkovic ◽  
Sasa Z. Zivkovic ◽  
Mirko S. Misljen
Keyword(s):  
Noise Removal ◽  
Control Law ◽  
State Variables ◽  
Linear Quadratic ◽  
State Variable ◽  
Guidance Law ◽  
Optimal Guidance ◽  
Differential Game Theory ◽  
Miss Distance ◽  
Guidance Laws

ABSTRACTThe paper presents a laser guided bomb guidance law based on the linear quadratic differential game theory, where a case of two perpendicular planes with two state variables in each plane has been considered. The Kalman filtering method has been used for noise removal from the measured signals and for estimation of the missing state variable values needed for the optimal guidance law. Optimisation has been conducted with respect to minimisation of the performance index. Comparative analysis of different guidance laws is done. A statistical analysis is performed to obtain the terminal miss distance in dependence on total flight time.

Active Control of Flexible Riser Vibration by Boundary Control Based on LQR Controller

2019 ◽  
Author(s):  
Jinxin Yu ◽  
Weimin Chen
Keyword(s):  
Boundary Control ◽  
Vibration Suppression ◽  
Lateral Displacement ◽  
Open Loop ◽  
Loop System ◽  
Ocean Current ◽  
Control Law ◽  
Flexible Riser ◽  
Linear Quadratic ◽  
Rotational Angle

Abstract The lateral displacement and the rotational angle of marine riser are likely to get larger as it is in stronger ocean current and, particularly, undergoes the consequences such as vortex-induced vibration or collisions between individual risers. The riser vibration with large amplitude value will lead to fatigue or coating damage of the structural body. In this study, the active vibration control, in terms of its angle and the displacement reductions, of a flexible riser under time-varying distributed load are considered using boundary control. The governing equations of the structural dynamics involving the control system of a flexible riser are built. The riser is modeled as an Euler-Bernoulli beam under the actions of ocean loads and the feedback controller. A torque actuator is introduced at the upper riser boundary, and the control law is employed to generate the required signal for riser angle control and displacement reduction. The feed-back control law is designed in state space, and the optimization of the control law is implemented based on the LQR approach. The linear quadratic regulator is used to determine the gain matrix, which can calculate the boundary control law by solving the Recatti equation. Based on the numerical simulations, the responses of the open-loop system and closed-loop system are presented and compared. The effectiveness of the vibration suppression of the flexible riser is examined.

Robust Piecewise-Linear State Observers for Flexible Link Mechanisms

2006 ◽  
Author(s):  
Roberto Caracciolo ◽  
Dario Richiedei ◽  
Alberto Trevisani
Keyword(s):  
Nonlinear Model ◽  
Closed Loop ◽  
Linear Models ◽  
Piecewise Linear ◽  
Equilibrium Points ◽  
Loop System ◽  
State Variables ◽  
Flexible Link ◽  
Closed Loop System ◽  
State Observers

This paper tackles the problem of designing state observers for flexible link mechanisms: an investigation is made on the possibility of employing observers making use of suitable piecewise-linear truncated dynamics models. A general approach is proposed, which provides an objective way of synthesizing observers preventing the instability that may arise from using reduced-order linearized models. The approach leads to the identification of the regions of the domain of the state variables where the linear approximations of the nonlinear model can be considered acceptable. To this purpose, first of all, the stability of the equilibrium points of the closed-loop system is assessed by applying the eigenvalue analysis to appropriate piecewise-linear models. Admittedly, the dynamics of such a closed-loop system is affected by the pole perturbation caused by spillover, and by the discrepancies between the linearized models of the plant and the one of the observer. Additionally, when nodal elastic displacements and velocities are not bounded in the infinitesimal neighborhoods of the equilibrium points, the difference between the nonlinear model and the locally-linearized one is expressed in terms of unstructured uncertainty and stability is assessed by H∞ robust analysis. The method is demonstrated by applying it to a closed-chain flexible link mechanism.

scholarly journals Composite Immersion and Invariance Based Adaptive Attitude Control of Asteroid-Orbiting Spacecraft in Elliptic Orbit

2021 ◽  
Author(s):  
Keum W Lee ◽  
Sahjendra N Singh
Keyword(s):  
Attitude Control ◽  
Closed Loop ◽  
Tracking Error ◽  
Loop System ◽  
Closed Loop System ◽  
Immersion And Invariance ◽  
State Dependent ◽  
Dependent Vector ◽  
Yaw Angle ◽  
Angle Tracking

Abstract This paper proposes a new composite noncertainty-equivalence adaptive (CNCEA) control system for the attitude (roll, pitch, and yaw angle) control of a spacecraft in an orbit around a uniformly rotating asteroid based on the immersion and invariance (I&I) theory. For the design, it is assumed that the asteroid's gravitational parameters and the spacecraft's inertia matrix are not known. In contrast to certainty-equivalence adaptive (CEA) or noncertainty-equivalence adaptive (NCEA) systems, the CNCEA attitude control system's composite identifier uses the attitude angle tracking error, a nonlinear state-dependent vector function, and model prediction error for parameter estimation. The Lyapunov analysis shows that in the closed-loop system, the Euler angles asymptotically track the reference attitude trajectories. Interestingly, there exist two parameter error-dependent attractive manifolds, to which the closed-loop system's trajectories converge. Moreover, the composite identifier using two types of error signals provides stronger stability properties in the closed-loop system. Simulation results are presented for the attitude control of a spacecraft orbiting in the vicinity of the asteroid 433 Eros. These results show precise nadir pointing attitude regulation, despite uncertainties in the system.

Immersion- and invariance-based adaptive missile control using filtered signals

2012 ◽  
Vol 226 (6) ◽  
pp. 646-663 ◽  
Author(s):  
K W Lee ◽  
S N Singh
Keyword(s):  
Control System ◽  
Closed Loop ◽  
Angle Of Attack ◽  
Loop System ◽  
Certainty Equivalent ◽  
Analytical Relation ◽  
Parametric Uncertainties ◽  
State Variables ◽  
Closed Loop System ◽  
Immersion And Invariance

The article presents a new non-certainty-equivalent adaptive (NCEA) longitudinal autopilot for the control of a missile based on the immersion and invariance theory. The interest here is to control the angle of attack of the missile in the presence of large parametric uncertainties. For the derivation of the control law, a backstepping design procedure is used. At each step of the design, certain filtered signals are generated for the synthesis of a stabilizing control signal and a parameter estimator. Using Lyapunov stability analysis, it is shown that in the closed-loop system, trajectory control of the angle of attack is accomplished, and the trajectories of the system are attracted to certain manifold in the space of state variables and parameter errors. For stability in the closed-loop system, an explicit analytical relation involving the controller gains is obtained. It may be pointed out that recently an adaptive autopilot based on the immersion and inversion theory has been designed, but it has stringent requirements because for its synthesis, the derivatives of the Mach number and angle of attack must be known, and a large number of parameters must be updated. The derived control system of this article is synthesized using only the state variables, and its identifier is of lower order. A traditional certainty-equivalent adaptive autopilot is also presented for comparison. Simulation results are obtained which show that the designed NCEA control system can accomplish angle of attack control despite large parametric uncertainties; and it can give better tracking performance than the traditional controller.

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