Estimation and Control of Dynamical Systems with Applications to Multi-Processor Systems
Sundaram, Shreyas (Adjunct) and Smith, Stephen L.
In this talk, we consider a set of estimation and control problems motivated by applications to next-generation multi-processor systems. We first study state estimation for linear systems with unknown inputs. When the system is not strongly detectable, one cannot exactly reconstruct the states without further information about the system or inputs. In this case, we consider two alternative settings: state norm estimation and state estimation for positive systems. The objective of state norm estimation is to construct an unknown input norm-observer which estimates an upper bound for the norm of the states. In order to characterize the existence of the norm observer, we propose a notion of bounded-input-bounded-output-bounded-state (BIBOBS) stability and provide necessary and sufficient conditions on the system matrices under which a linear system is BIBOBS stable. For the second setting, as a negative result, we show that the additional information on positivity is not helpful in relaxing the conditions under which perfect estimation is achievable.
Next we consider the problem of selecting an optimal set of sensors to estimate the states of linear dynamical systems. The goal is to choose at design-time a subset of sensors (satisfying certain budget constraints) from a given set in order to minimize the trace of the steady state a priori or a posteriori error covariance produced by a Kalman filter. We show that the a priori and a posteriori error covariance-based sensor selection problems are both NP-hard, even under the additional assumption that the system is stable. We then provide bounds on the worst-case performance of sensor selection algorithms based on the system dynamics, and study greedy algorithms and corresponding variants for the sensor selection problems.
Finally, we study the output tracking problem for nonlinear systems with constraints. In order for the system output to track a class of piecewise-constant reference signals with limited online computational resources, we propose a sampling-based explicit nonlinear model predictive control (ENMPC) approach, where only a bound on the admissible references is known to the designer a priori. The basic idea of sampling-based ENMPC is to sample the state and reference signal space using deterministic sampling and construct the ENMPC by using regression methods. The proposed approach guarantees feasibility and stability for all admissible references and ensures asymptotic convergence to the set-point. Furthermore, we propose a robust variant of the sampling-based ENMPC for the case where there is an additive bounded disturbance.