Multiple Loop Self-Triggered Model Predictive Control for Network Scheduling and Control

We present an algorithm for controlling and scheduling multiple linear time-invariant processes on a shared bandwidth limited communication network using adaptive sampling intervals. The controller is centralized and computes at every sampling instant not only the new control command for a process, but also decides the time interval to wait until taking the next sample. The approach relies on model predictive control ideas, where the cost function penalizes the state and control effort as well as the time interval until the next sample is taken. The latter is introduced in order to generate an adaptive sampling scheme for the overall system such that the sampling time increases as the norm of the system state goes to zero. The paper presents a method for synthesizing such a predictive controller and gives explicit sufficient conditions for when it is stabilizing. Further explicit conditions are given which guarantee conflict free transmissions on the network. It is shown that the optimization problem may be solved off-line and that the controller can be implemented as a lookup table of state feedback gains. Simulation studies which compare the proposed algorithm to periodic sampling illustrate potential performance gains.Comment: Accepted for publication in IEEE Transactions on Control Systems Technolog

A Finite-Time Cutting Plane Algorithm for Distributed Mixed Integer Linear Programming

Many problems of interest for cyber-physical network systems can be formulated as Mixed Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithm to solve this class of optimization problems in a peer-to-peer network with no coordinator and with limited computation and communication capabilities. In the proposed algorithm, at each communication round, agents solve locally a small LP, generate suitable cutting planes, namely intersection cuts and cost-based cuts, and communicate a fixed number of active constraints, i.e., a candidate optimal basis. We prove that, if the cost is integer, the algorithm converges to the lexicographically minimal optimal solution in a finite number of communication rounds. Finally, through numerical computations, we analyze the algorithm convergence as a function of the network size.Comment: 6 pages, 3 figure

Tractable robust MPC design based on nominal predictions

Many popular approaches in the field of robust model predictive control (MPC) are based on nominal predictions. This paper presents a novel formulation of this class of controller with proven input-to-state stability and robust constraint satisfaction. Its advantages are: (i) the design of its main ingredients are tractable for medium to large-sized systems, (ii) the terminal set does not need to be robust with respect to all the possible system uncertainties, but only for a reduced set that can be made arbitrarily small, thus facilitating its design and implementation, (iii) under certain conditions the terminal set can be taken as a positive invariant set of the nominal system, allowing us to use a terminal equality constraint, which facilitates its application to large-scale systems, and (iv) the complexity of its optimization problem is comparable to the non-robust MPC variant. We show numerical closed-loop results of its application to a multivariable chemical plant and compare it against other robust MPC formulations.Ministerio de Ciencia e Innovación - Agencia Estatal de Investigación PID2019-106212 RB-C41Junta de Andalucía - Fondo Europeo de Desarrollo Regional P20_00546Ministerio de Ciencia e Innovación - Agencia Estatal de Investigación PDC2021-121120-C2

Imprecise dynamic walking with time-projection control

We present a new walking foot-placement controller based on 3LP, a 3D model of bipedal walking that is composed of three pendulums to simulate falling, swing and torso dynamics. Taking advantage of linear equations and closed-form solutions of the 3LP model, our proposed controller projects intermediate states of the biped back to the beginning of the phase for which a discrete LQR controller is designed. After the projection, a proper control policy is generated by this LQR controller and used at the intermediate time. This control paradigm reacts to disturbances immediately and includes rules to account for swing dynamics and leg-retraction. We apply it to a simulated Atlas robot in position-control, always commanded to perform in-place walking. The stance hip joint in our robot keeps the torso upright to let the robot naturally fall, and the swing hip joint tracks the desired footstep location. Combined with simple Center of Pressure (CoP) damping rules in the low-level controller, our foot-placement enables the robot to recover from strong pushes and produce periodic walking gaits when subject to persistent sources of disturbance, externally or internally. These gaits are imprecise, i.e., emergent from asymmetry sources rather than precisely imposing a desired velocity to the robot. Also in extreme conditions, restricting linearity assumptions of the 3LP model are often violated, but the system remains robust in our simulations. An extensive analysis of closed-loop eigenvalues, viable regions and sensitivity to push timings further demonstrate the strengths of our simple controller

Aperiodic Communication for MPC in Autonomous Cooperative Landing

In this paper, we focus on the rendezvous problem for the autonomous cooperative landing of an unmanned aerial vehicle (UAV) on an unmanned surface vehicle (USV). These heterogeneous agents with nonlinear dynamics are dynamically decoupled but share a common cooperative rendezvous task. The underlying control scheme is based on the Distributed Model Predictive Control (MPC). One of our main contributions is a rendezvous algorithm with an online update rule of the rendezvous location. The algorithm requires that agents update the rendezvous location only when they are not guaranteed to reach it. Therefore, the exchange of information occurs aperiodically and proposed algorithm improves the communication efficiency. Furthermore, we prove the recursive feasibility of the algorithm. The simulation results show the effectiveness of our algorithm applied to the problem of autonomous cooperative landing.Comment: 7 pages, 6 figures, This work has been submitted to IFAC for possible publication, 7th IFAC Conference on Nonlinear Model Predictive Control 202