187 research outputs found
LQG control with missing observation and control packets
Abstract: The paper considers the Linear Quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when data loss may occur between the sensors and the estimation-control unit and between the latter and the actuation points. For protocols where packets are acknowledged at the receiver (e.g. TCP type protocols), the separation principle holds. Moreover, the optimal LQG control is a linear function of the state. Finally, building upon our previous results on estimation with unreliable communication, the paper shows the existence of critical arrival probabilities below which the optimal controller fails to stabilize the system. This is done by providing analytic upper and and lower bounds on the cost functional, and stochastically characterizing their convergence properties in the infinite horizon. More interestingly, it turns out that when there is no feedback on whether a control packet has been delivered or not(e.g. UDP type protocols), the LQG optimal controller is in general nonlinear. A special case when the optimal controller is indeed linear is shown
Optimal estimation and control for lossy network: stability, convergence, and performance
In this paper, we study the problems of optimal estimation and control, i.e., the linear quadratic Gaussian (LQG) control, for systems with packet losses but without acknowledgment. Such acknowledgment is a signal sent by the actuator to inform the estimator of the incidence of control packet losses. For such system, which is usually called as a user datagram protocol (UDP)-like system, the optimal estimation is nonlinear and its calculation is time-consuming, making its corresponding optimal LQG problem complicated. We first propose two conditions: 1) the sensor has some computation abilities; and 2) the control command, exerted to the plant, is known to the sensor. For a UDP-like system satisfying these two conditions, we derive the optimal estimation. By constructing the finite and infinite product probability measure spaces for the estimation error covariances (EEC), we give the stability condition for the expected EEC, and show the existence of a measurable function to which the EEC converges in distribution, and propose some practical methods to evaluate the estimation performance. Finally, the LQG controllers are derived, and the conditions for the mean square stability of the closed-loop system are established
Output feedback stochastic MPC with packet losses
The paper considers constrained linear systems with stochastic additive
disturbances and noisy measurements transmitted over a lossy communication
channel. We propose a model predictive control (MPC) law that minimizes a
discounted cost subject to a discounted expectation constraint. Sensor data is
assumed to be lost with known probability, and data losses are accounted for by
expressing the predicted control policy as an affine function of future
observations, which results in a convex optimal control problem. An online
constraint-tightening technique ensures recursive feasibility of the online
optimization and satisfaction of the expectation constraint without bounds on
the distributions of the noise and disturbance inputs. The cost evaluated along
trajectories of the closed loop system is shown to be bounded by the optimal
predicted cost. A numerical example is given to illustrate these results
Stochastic output feedback MPC with intermittent observations
This paper considers constrained linear systems with stochastic additive
disturbances and noisy measurements transmitted over a lossy communication
channel. We propose a model predictive control (MPC) law that minimises a
discounted cost subject to a discounted expectation constraint. Sensor data is
assumed to be lost with known probability, and data losses are accounted for by
expressing the predicted control policy as an affine function of future
observations, which results in a convex optimal control problem. An online
constraint-tightening technique ensures recursive feasibility of the online
optimisation problem and satisfaction of the expectation constraint without
imposing bounds on the distributions of the noise and disturbance inputs. The
discounted cost evaluated along trajectories of the closed loop system is shown
to be bounded by the initial optimal predicted cost. We also provide conditions
under which the averaged undiscounted closed loop cost accumulated over an
infinite horizon is bounded. Numerical simulations are described to illustrate
these results.Comment: 12 pages. arXiv admin note: substantial text overlap with
arXiv:2004.0259
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