12 results on '"TRAJECTORY optimization"'
Search Results
2. Stability and Performance Analysis for Positive Fractional-Order Systems With Time-Varying Delays.
- Author
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Shen, Jun and Lam, James
- Subjects
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FRACTIONAL differential equations , *TIME-varying systems , *FUNCTIONS of bounded variation , *TRAJECTORY optimization , *STABILITY of linear systems - Abstract
This paper addresses the stability and L\infty-gain analysis problem for continuous-time positive fractional-order delay systems with incommensurate orders between zero and one. A necessary and sufficient condition is firstly given to characterize the positivity of continuous-time fractional-order systems with bounded time-varying delays. Moreover, by exploiting the monotonic and asymptotic property of the constant delay system by virtue of the positivity, and comparing the trajectory of the time-varying delay system with that of the constant delay system, it is proved that the asymptotic stability of positive fractional-order systems is not sensitive to the magnitude of delays. In addition, it is shown that the L\infty-gain of a positive fractional-order system is independent of the magnitude of delays and fully determined by the system matrices. Finally, a numerical example is given to show the validity of the theoretical results. [ABSTRACT FROM PUBLISHER]
- Published
- 2016
- Full Text
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3. MPC for Tracking Periodic References.
- Author
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Limon, Daniel, Pereira, Mario, Munoz de la Pena, David, Alamo, Teodoro, Jones, Colin N., and Zeilinger, Melanie N.
- Subjects
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PREDICTIVE control systems , *CLOSED loop systems , *SYSTEMS design , *CONSTRAINT satisfaction , *TRAJECTORY optimization - Abstract
In this technical note, a new model predictive controller for tracking arbitrary periodic references is presented. The proposed controller is based on a single layer that unites dynamic trajectory planning and control. A design procedure to guarantee that the closed loop system converges asymptotically to the optimal admissible periodic trajectory while guaranteeing constraint satisfaction is provided. In addition, the constraints of the optimization problem solved by the controller do not depend on the reference, allowing for sudden changes in the reference without loosing feasibility. The properties of the proposed controller are demonstrated with a simulation example of a ball and plate system. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
4. A Method of Estimating the Domain of Attraction for Nonlinear Discrete-Time Systems.
- Author
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Jerbi, Houssem, Braiek, Naceur, and Bacha, Anis
- Subjects
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LYAPUNOV functions , *ASYMPTOTIC distribution , *POLYNOMIALS , *DISCRETE groups , *TRAJECTORY optimization - Abstract
This paper investigates the problem of estimating an asymptotic stability region of nonlinear polynomial discrete-time systems. To achieve an appropriate estimation of subsets of attraction regions for asymptotically stable equilibrium points, the reverse trajectory formalism is applied through the formulation of iterative algorithms. The developed methods enable us to obtain enlarged circular domains of attraction that are comparable with the ones obtained by delicate computational procedures. The main advantage of the synthesized algorithms is that they disregard the problem of constructing Lyapunov function to achieve the control target for nonlinear systems. An instructive example of a power electrical system is used as an illustration of the results of the synthesized approaches. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
5. Asymptotically stable biped gait generation based on stability principle of rimless wheel.
- Author
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Asano, Fumihiko and Zhi-Wei Luo
- Subjects
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EQUILIBRIUM , *MECHANICAL engineering , *STOPPING power (Nuclear physics) , *COMPUTER simulation , *TRAJECTORY optimization , *ASYMPTOTIC expansions - Abstract
We investigated and identified the conditions necessary for stable dynamic gait generation in biped robots from the mechanical energy balance point of view. The equilibrium point at impact in a dynamic gait is uniquely determined by two conditions; keeping the restored mechanical energy constant and settling the relative hip-joint angle to the desired value before impact. The generated gait then becomes asymptotically stable around the equilibrium point determined by these conditions. This is shown by a simple recurrence formula of the kinetic energy immediately before impact. We verified this stability theorem using numerical simulation of virtual passive dynamic walking. The results were compared with those for a rimless wheel and an inherent stability principle was derived. Finally, we derived a robust control law using a reference mechanical energy trajectory and demonstrated its effectiveness numerically. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
6. Vector Field Path Following for Miniature Air Vehicles.
- Author
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Nelson, Derek R., Barber, D. Blake, McLain, Timothy W., and Beard, Randal W.
- Subjects
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VECTOR fields , *VECTOR analysis , *LYAPUNOV functions , *DRONE aircraft , *TRAJECTORY optimization - Abstract
In this paper, a method for accurate path following for miniature air vehicles is developed. The method is based on the notion of vector fields, which are used to generate desired course inputs to inner-loop attitude control laws. Vector-field path-following control laws are developed for straight-line paths and circular arcs and orbits. Lyapunov stability arguments are used to demonstrate asymptotic decay of path-following errors in the presence of constant wind disturbances. Experimental flight tests have demonstrated mean path-following errors on less than one wingspan for straight-line and orbit paths and less than three wingspans for paths with frequent changes in direction. [ABSTRACT FROM PUBLISHER]
- Published
- 2007
- Full Text
- View/download PDF
7. Quantitative Studies on Asymptotic Growth Behaviors of Trajectories of Nonlinear Discrete Dynamical Systems.
- Author
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Wang, Lisheng and Xu, Zongben
- Subjects
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NONLINEAR dynamical systems , *CONTROL theory (Engineering) , *NONLINEAR operators , *TRAJECTORY optimization , *ESTIMATION theory , *DISCRETE systems - Abstract
This technical note studies quantitatively asymptotic growth behaviors of trajectories (AGBT) of nonlinear autonomous discrete dynamical system that has unbounded domain, non-Lipschitz continuous nonlinear operator, and stable or unstable equilibrium point. We explain how trajectory motion speed is quantitatively determined in the system, and study exact computation and sharp estimation of the smallest exponential bound of trajectories. We characterize exponential stability and asymptotic stability of the system from a new point of view, and provide a simple condition to distinguish them from each other. These results extend existing results that were obtained in some special cases of the system, and are helpful for quantitative analysis and understanding of AGBT of the system. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
8. Lyapunov Theory for 2-D Nonlinear Roesser Models: Application to Asymptotic and Exponential Stability.
- Author
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Yeganefar, Nima, Yeganefar, Nader, Ghamgui, Mariem, and Moulay, Emmanuel
- Subjects
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EXPONENTIAL stability , *NONLINEAR statistical models , *LYAPUNOV functions , *ASYMPTOTIC controllability , *TRANSFER functions , *DISCRETE systems , *LINEAR systems , *TRAJECTORY optimization - Abstract
This technical note deals with a general class of discrete 2-D possibly nonlinear systems based on the Roesser model. We first motivate the introduction of Lyapunov type definitions of asymptotic and exponential stability. This will allow us to introduce and discuss several particularities that cannot be found in 1-D systems. Once this background has been carefully designed, we develop different Lyapunov theorems in order to check asymptotic and exponential stability of nonlinear 2-D systems. Finally we propose the first converse Lyapunov theorem in the case of exponential stability. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
9. Distributed Receding Horizon Control of Vehicle Platoons: Stability and String Stability.
- Author
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Dunbar, William B. and Caveney, Derek S.
- Subjects
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NONLINEAR theories , *ALGORITHMS , *SIMULATION methods & models , *TRAJECTORY optimization , *ROBOTIC path planning , *INTELLIGENT transportation systems - Abstract
This paper considers the problem of distributed control of a platoon of vehicles with nonlinear dynamics. We present distributed receding horizon control algorithms and derive sufficient conditions that guarantee asymptotic stability, leader-follower string stability, and predecessor-follower string stability, following a step speed change in the platoon. Vehicles compute their own control in parallel, and receive communicated position and velocity error trajectories from their immediate predecessor. Leader-follower string stability requires additional communication from the lead car at each update, in the form of a position error trajectory. Predecessor-follower string stability, as we define it, implies leader-follower string stability. Predecessor-follower string stability requires stricter constraints in the local optimal control problems than the leader-follower formulation, but communication from the lead car is required only once at initialization. Provided an initially feasible solution can be found, subsequent feasibility of the algorithms are guaranteed at every update. The theory is generalized for nonlinear decoupled dynamics, and is thus applicable to fleets of planes, robots, or boats, in addition to cars. A simple seven-car simulation examines parametric tradeoffs that affect stability and string stability. Analysis on platoon formation, heterogeneity and size (length) is also considered, resulting in intuitive tradeoffs between lead car and following car control flexibility. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
10. Stability-Preserving Optimization in the Presence of Fast Disturbances.
- Author
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Wirth, Benedikt, Gerhard, Johannes, and Marquardt, Wolfgang
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STABILITY (Mechanics) , *ROBUST optimization , *TRAJECTORY optimization , *MANIFOLDS (Mathematics) , *ASYMPTOTIC symmetry (Physics) , *DYNAMICS , *PARAMETERS (Statistics) - Abstract
We present algebraic conditions on the trajectory of a dynamical system to approximately describe a certain type of system robustness. The corresponding equations can be used as constraints in a robust optimization procedure to select a set of optimal design parameters for a dynamical system which is subject to fast disturbances. Robustness is ensured by requiring the disturbance parameters to stay sufficiently far away from critical manifolds in the disturbance parameter space, at which the system would lose stability. The closest distance to the critical manifolds is measured along their normal vectors. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
11. Combination of Lyapunov and Density Functions for Stability of Rotational Motion.
- Author
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Vasconcelos, José Fernandes, Rantzer, Anders, Silvestre, Carlos, and Oliveira, Paulo Jorge
- Subjects
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LYAPUNOV functions , *DENSITY functionals , *ROTATIONAL motion , *NONLINEAR systems , *TRAJECTORY optimization , *OBSERVABILITY (Control theory) , *NOISE - Abstract
Lyapunov methods and density functions provide dual characterizations of the solutions of a nonlinear dynamic system. This work exploits the idea of combining both techniques, to yield stability results that are valid for almost all the solutions of the system. Based on the combination of Lyapunov and density functions, analysis methods are proposed for the derivation of almost input-to-state stability, and of almost global stability in nonlinear systems. The techniques are illustrated for an inertial attitude observer, where angular velocity readings are corrupted by non-idealities. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
12. Backstepping Design for Incremental Stability.
- Author
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Zamani, Majid and Tabuada, Paulo
- Subjects
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NONLINEAR systems , *STABILITY (Mechanics) , *MATHEMATICAL models , *CONTROL theory (Engineering) , *SYNCHRONIZATION , *MATRIX inequalities , *TRAJECTORY optimization - Abstract
Stability is arguably one of the core concepts upon which our understanding of dynamical and control systems has been built. The related notion of incremental stability, however, has received much less attention until recently, when it was successfully used as a tool for the analysis and design of intrinsic observers, output regulation of nonlinear systems, frequency estimators, synchronization of coupled identical dynamical systems, symbolic models for nonlinear control systems, and bio-molecular systems. However, most of the existing controller design techniques provide controllers enforcing stability rather than incremental stability. Hence, there is a growing need to extend existing methods or develop new ones for the purpose of designing incrementally stabilizing controllers. In this technical note, we develop a backstepping design approach for incremental stability. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
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