September 2021
September 16th - 14h (Salle Europe)
Speaker : Thomas Conord (PhD student with Dimitri Peaucelle)
Title : Continuous quaternion based almost global attitude tracking
Abstract : This paper considers the attitude control problem of a generic rotating 3 degrees of freedom fully actuated rigid object. The specific studied problem is the deviation control of this object around a theoretically feasible attitude trajectory. The rotation motion has an intrinsic non linear behaviour (trigonometric, 2-periodicity) that need to build non linear and hybrid controllers to get global stability of the closed loop system. This paper considers the opportunity to use the quaternion framework to build a continuous non linear state feedback that reaches an almost global asymptotical stability. Some perspectives to enhance this result with integrators to cancel out static and drag errors are eventually proposed.
Title : Continuous quaternion based almost global attitude tracking
Abstract : This paper considers the attitude control problem of a generic rotating 3 degrees of freedom fully actuated rigid object. The specific studied problem is the deviation control of this object around a theoretically feasible attitude trajectory. The rotation motion has an intrinsic non linear behaviour (trigonometric, 2-periodicity) that need to build non linear and hybrid controllers to get global stability of the closed loop system. This paper considers the opportunity to use the quaternion framework to build a continuous non linear state feedback that reaches an almost global asymptotical stability. Some perspectives to enhance this result with integrators to cancel out static and drag errors are eventually proposed.
Speaker : Lina Guan (invited PhD student from Gipsa-Lab, Grenoble)
Title : Optimization for Heterogenous Traffic Flow with Bottleneck
Abstract : This paper develops an optimal observer-based output feedback control law in order to dissolve traffic congestion resulting from traffic breakdown. The macroscopic second-order N-class Aw-Rascle-Zhang (ARZ) traffic model consists of 2N hyperbolic partial differential equations (PDEs) describing the congested traffic dynamics on freeways. Each vehicle class charaterized by its own vehicle size and driver's behavior. After linearizing the model equations around steady states, it is observed that in the congested traffic, m characteristic speeds are positive, whereas the remaining 2N-m are negative. The backstepping method is employed to stabilize the 2NX2N hetero-directional hyperbolics PDEs. The control input actuates the traffic flow at the inlet boundary of the inverstigated road section and is implemented by a ramp metering. The output feedback controller is obtained by designing a collocated observer and combining it with full state feedback. The output feedback control law achieves to dissolve the traffic congestion in finite time by measuring the velocities and inflows of all vehicle classes at the inlet of the considered road section. The performance of stabilization is verified by simulating the linearized model and the highest road throughput is achieved.
Title : Optimization for Heterogenous Traffic Flow with Bottleneck
Abstract : This paper develops an optimal observer-based output feedback control law in order to dissolve traffic congestion resulting from traffic breakdown. The macroscopic second-order N-class Aw-Rascle-Zhang (ARZ) traffic model consists of 2N hyperbolic partial differential equations (PDEs) describing the congested traffic dynamics on freeways. Each vehicle class charaterized by its own vehicle size and driver's behavior. After linearizing the model equations around steady states, it is observed that in the congested traffic, m characteristic speeds are positive, whereas the remaining 2N-m are negative. The backstepping method is employed to stabilize the 2NX2N hetero-directional hyperbolics PDEs. The control input actuates the traffic flow at the inlet boundary of the inverstigated road section and is implemented by a ramp metering. The output feedback controller is obtained by designing a collocated observer and combining it with full state feedback. The output feedback control law achieves to dissolve the traffic congestion in finite time by measuring the velocities and inflows of all vehicle classes at the inlet of the considered road section. The performance of stabilization is verified by simulating the linearized model and the highest road throughput is achieved.
September 9th - 15h (Salle Europe) - Répétition de thèse
Speaker : Thomas Conord (PhD student with Dimitri Peaucelle)
Title : Contrôle robuste des systèmes variant dans le temps - Application au contrôle d'attitude modélisée par quaternion
Abstract : This PhD thesis proposes methods of analysis and controller synthesis for Linear Time Varying systems. It considers the opportunity to extend to these systems the notions of poles location and input/output performance analysis dedicated to Linear Time Invariant systems. The proposed method concerns systems which varying parameters can be bounded inside a convex set described by a polytope. It enables to write as Linear Matrix Inequalities the problems of analysis and of static state feedback synthesis for these time-varying systems. A direct extension of these results can be made for systems which state space representation does not only have the property to be time-varying, but may also have the property of being nonlinear functions, possibly discontinuous, of the states and inputs, assuming these state matrices are bounded inside a polytope. This last result is eventually applied to the attitude control of a fully actuated three degrees of freedom rotating object, which rotational movement is modeled with the unit quaternion.
Title : Contrôle robuste des systèmes variant dans le temps - Application au contrôle d'attitude modélisée par quaternion
Abstract : This PhD thesis proposes methods of analysis and controller synthesis for Linear Time Varying systems. It considers the opportunity to extend to these systems the notions of poles location and input/output performance analysis dedicated to Linear Time Invariant systems. The proposed method concerns systems which varying parameters can be bounded inside a convex set described by a polytope. It enables to write as Linear Matrix Inequalities the problems of analysis and of static state feedback synthesis for these time-varying systems. A direct extension of these results can be made for systems which state space representation does not only have the property to be time-varying, but may also have the property of being nonlinear functions, possibly discontinuous, of the states and inputs, assuming these state matrices are bounded inside a polytope. This last result is eventually applied to the attitude control of a fully actuated three degrees of freedom rotating object, which rotational movement is modeled with the unit quaternion.