On the observer canonical form for Nonlinear Time-Delay Systems

6 pagesInternational audienceNecessary and sufficient geometric conditions for the equivalence of a nonlinear time-delay system with one output, under bicausal change of coordinates and output transformation, to a linear weakly observable time-delay system up to output injection are given. These conditions are derived through the use of the Extended Lie Bracket operator recently introduced in the literature for dealing with time-delay systems. The results presented show how this operator is useful in the analysis of this class of nonlinear systems

Unbiased Filtering for State and Unknown Input with Delay

International audienceIn this paper, we consider linear network systems with unknown inputs. We present an unbiased recursive algorithm that simultaneously estimates states and inputs. We focus on delay-left invertible systems with intrinsic delay l ≥ 1, where the input reconstruction is possible only by using outputs up to l time steps later in the future. By showing an equivalence with a descriptor system, we state conditions under which the time-varying filter converges to a stationary stable filter, involving the solution of a discrete-time algebraic Riccati equation

Team decision theory for linear continuous-time systems

This paper develops a team decision theory for linear-quadratic (LQ) continuous-time systems. First, a counterpart of the well-known result of Radner on quadratic static teams is obtained for two-member continuous-time LQ static team problems when the statistics of the random variables involved are not necessarily Gaussian. An iterative convergent scheme is developed, which in the limit yields the optimal team strategies. For the special case of Gaussian distributions, the team-optimal solution is affine in the information available to each DM, and for the further special case when the team cost function does not penalize the intermediate values of state, the optimal strategies can be obtained by solving a Liapunov type time-invariant matrix equation. This static theory is then extended to LQG continuous-time dynamic teams with sampled observations under the one-step-delay observation sharing pattern. The unique solution is again affine in the information available to each DM, and further, it features a certainty-equivalence property

Unbiased Filtering for State and Unknown Input with Delay

International audienceIn this paper, we consider linear network systems with unknown inputs. We present an unbiased recursive algorithm that simultaneously estimates states and inputs. We focus on delay-left invertible systems with intrinsic delay l ≥ 1, where the input reconstruction is possible only by using outputs up to l time steps later in the future. By showing an equivalence with a descriptor system, we state conditions under which the time-varying filter converges to a stationary stable filter, involving the solution of a discrete-time algebraic Riccati equation

Delay-Adaptive Boundary Control of Coupled Hyperbolic PDE-ODE Cascade Systems

This paper presents a delay-adaptive boundary control scheme for a $2\times 2$ coupled linear hyperbolic PDE-ODE cascade system with an unknown and arbitrarily long input delay. To construct a nominal delay-compensated control law, assuming a known input delay, a three-step backstepping design is used. Based on the certainty equivalence principle, the nominal control action is fed with the estimate of the unknown delay, which is generated from a batch least-squares identifier that is updated by an event-triggering mechanism that evaluates the growth of the norm of the system states. As a result of the closed-loop system, the actuator and plant states can be regulated exponentially while avoiding Zeno occurrences. A finite-time exact identification of the unknown delay is also achieved except for the case that all initial states of the plant are zero. As far as we know, this is the first delay-adaptive control result for systems governed by heterodirectional hyperbolic PDEs. The effectiveness of the proposed design is demonstrated in the control application of a deep-sea construction vessel with cable-payload oscillations and subject to input delay

Offset-free model predictive control: a study of different formulations with further results

This paper presents discussions on offset-free model predictive control (MPC) methods for linear discrete-time systems in the presence of deterministic system disturbances. The general approach is based on the use of a disturbance model and an observer to estimate the disturbance states. The recent development in offset-free MPC has established the equivalence of the velocity form (without output delay) to a specific choice of the disturbance model and observer. In this note, it was shown that this particular disturbance model and observer is not necessarily equivalent to the velocity form with output delay. Nevertheless, it was shown that the velocity form with output delay is equivalent to a different choice of the disturbance model and observer. An import of this result is that the velocity forms (with and without delayed output) belong to the same general approach - disturbance model and observer. Furthermore, areas that may be considered in future researches are also highlighted