Vladislav Nenchev

Minimax Model Predictive Operation Control of Microgrids

Abstract Due to the steady growth of decentralised distributed generation, the operational management of small, local electricity networks (microgrids) is becoming an increasing challenge to meet: How to provide an operational control for microgrids with a high share of renewable energy sources (RES) that is robust to perturbations? In this paper we address an optimal control problem (OCP) that maintains all of the stated properties in the presence of an uncertain load and RES infeed in islanded operation. Assuming that the uncertainty is within a bounded region along a given load and RES trajectory prediction, the problem is posed as a worst-case hybrid OCP, where the RES output can be curtailed. We propose a minimax (MM) model predictive control (MPC) scheme that adjusts according to the present uncertainty and can be formulated as a mixed-integer linear program (MILP) and solved numerically online.

Optimal motion planning with temporal logic and switching constraints

This paper proposes a method for automatic generation of time-optimal robot motion trajectories for the task of collecting and moving a finite number of objects to particular spots in space, while maintaining predefined temporal logic constraints. The continuous robot dynamics change upon an object pick-up or drop-off. The temporal constraints are expressed as syntactically co-safe Linear Temporal Logic (scLTL) formulas over the set of object and drop-off sites. We propose an approach based on constructing a discrete abstraction of the hybrid system modeling the robot in the form of a finite weighted transition system. Then, by employing tools from automata-based model checking, we obtain an automaton containing only paths that satisfy the specification. The shortest path in this automaton is found by graph search and corresponds directly to the time-optimal hybrid trajectory. The method is applied to a case study with a mobile ground robot and a case study involving a quadrotor moving in an environment with obstacles, thus reflecting its computational advantage over a direct optimization approach.

Towards time-optimal exploration and control by an autonomous robot

In this paper, we address the problem of an autonomous robotic vehicle collecting a finite but unknown number of objects with non-negligible masses and unknown locations in a restricted area and moving them to a particular spot in minimum time. An adaptive certainty-equivalent navigation and control policy is introduced based on a pick-up and an exploration/drop-off mode. While the input signal in pickup mode is easily obtained in real time, complete exploration and drop-off corresponds to a hybrid optimal control problem (OCP) with exponential complexity in the finitely discretized space. We propose a trajectory planning algorithm by restricting the motion of the robot to a finite weighted graph. Further, we describe a discrete-time approximation of the hybrid OCP and compare both approaches with respect to computational complexity and accuracy.

Distributed State Estimation for Hybrid and Discrete Event Systems Using l-Complete Approximations

Abstract The topic of this paper is distributed state estimation for time-invariant systems with finite input and output spaces. We assume that the system under investigation can be realised by a hybrid I/S/O-machine, where some of the discrete states may also represent failure modes. Our approach is based on previous work, e.g., Moor and Raisch (1999); Moor et al. (2002), where l-complete approximations were proposed as discrete event abstractions for hybrid dynamical systems. In particular, it has been shown that l-complete approximations can be used to provide set-valued estimates for the unknown system state. Estimates are conservative in the sense that the true state can be guaranteed to be contained in the set-valued estimate. In this contribution, we show that for a class of hybrid systems the same estimate can be obtained via a distributed, or decentralised, approach involving several less complex approximations, which are run in parallel. For a larger class of systems, it can be shown that this approach provides an outer approximation of the estimate provided by a monolithic l-complete estimator. The proposed procedure implies significant computational savings during estimator synthesis, with an only modest increase in on-line effort. The latter is a result of “assembling” the global estimate from the available local estimates. The resulting computational trade-off is explicitly discussed.

Optimal exploration and control for a robotic pick-up and delivery problem

In this paper we address a problem where a robot moving on a line has to find and collect a finite number of objects and move them to a specified point. The robot is modeled as a second-order system and the task has to be completed in minimum time. Both the robot and the objects are represented by point masses. The objects are located at unknown places within a given interval and their pick-up and drop-off leads to a switching of the dynamics. The corresponding hybrid Optimal Control Problem (OCP) is investigated for the worst-case and a probabilistic case assuming a uniform distribution of the objects over the interval. We first derive optimal solutions for a single object. Then, we show that an optimal solution for the multi-object case consists of complete exploration followed by a deterministic optimal pick-up and drop-off (with possible intermediate drop-offs) of all objects. Thus, the computation of the exploration and the exploitation part of the control can be decoupled, similar to the single object case. The worst- and the probabilistic case optimal solutions are compared in a numerical example. The proposed methods are particularly relevant for different robotic applications like automated cleaning, search and rescue, harvesting, manufacturing etc.

Approximate closed-loop minimax model predictive operation control of microgrids

We address an optimal control problem for a microgrid in islanded operation with bounded uncertain load and renewable infeed. While model predictive control (MPC) with worst-case cost evaluation is often employed to obtain robust optimal control laws in the presence of bounded disturbances, it suffers from an inherent conservativeness. To counteract this phenomenon, we propose an approximate closed-loop minimax MPC scheme, where the renewable energy sources output can be curtailed. The MPC is formulated as a mixed-integer linear program, solved online and applied in a receding horizon fashion. In the case study, the approximate closed-loop approach yields a better prediction accuracy and performance than the corresponding open-loop scheme.

Optimal exploration and control for a robotic pick-up and delivery problem in two dimensions

This paper addresses an optimal control problem for a robot that has to find and collect a finite number of objects and move them to a depot in minimum time. The objects are modeled by point masses with a priori unknown locations in a bounded two-dimensional space. The robot has forth-order dynamics that change instantaneously at any pick-up or drop-off of an object. The corresponding hybrid Optimal Control Problem (OCP) is solved by a receding horizon scheme, where the derived lower bound for the cost-to-go is evaluated for the worst- and a probabilistic case, assuming a uniform distribution of the objects. We first present a time-driven approximate solution based on time and position space discretization. Due to the high computational cost of this solution, we alternatively propose an event-driven approximate approach based on a suitable motion parameterization. The solutions are compared in a numerical example, suggesting that the latter approach offers a significant computational advantage while yielding similar qualitative results compared to the former.

Receding horizon robot control in partially unknown environments with temporal logic constraints

This paper addresses the control of a mobile robot that has to accomplish a finite task in a partially unknown static environment in minimum time. The task is expressed as a syntactically co-safe Linear Temporal Logic (scLTL) formula over a set of properties that can be satisfied at the regions of a partitioned environment. The robot discovers a-priori unknown properties upon covering the corresponding region by its limited sensing range. Instead of resorting to an abstraction of the hybrid system modeling the robots motion in the environment, we propose an approach based on parameterizing the continuous motion of the vehicle and introduce a measure of violation that is used to enforce the satisfaction of the specification. Then, we formulate a parametric Optimal Control Problem (OCP), where the objective is a convex combination of the overall time and the measure of violation function. The OCP is solved in a receding horizon manner only upon detecting previously unknown properties of the environment. The approach is illustrated with a numerical case study.

Optimal adaptive predictive control of a combustion engine

This paper deals with the optimal tracking control of a spark ignited combustion engine. The overall controller consists of an (a priori given) feed-forward part that steers the system close to the desired trajectory and an optimal adaptive predictive controller for the tracking error dynamics. The latter is based on estimating a linear model along the desired trajectory online, which is then used in a model predictive control (MPC) scheme that systematically incorporates the input and state constraints in the design process. The provided feed-forward control and its respective combination with an infinite linear-quadratic regulator (LQR) and the adaptive MPC are compared in simulation. The results demonstrate a decrease in fuel consumption at the price of a minor performance loss in terms of tracking the desired torque cycle, while avoiding disadvantageous operation of the engine at all times.

Decentralized set-valued state estimation based on non-deterministic chains

A general decentralized computational framework for set-valued state estimation and prediction for systems that assume a hybrid state machine representation is introduced in this article. The decentralized scheme consists of a conjunction of a finite set of distributed state machines that are specified by a decomposition of the external signal space. While, in general, the latter is shown to be an outer approximation of the corresponding outcome of the original state machine, here, specific rules for the signal space decomposition are devised by utilizing structural properties of the underyling transition relation, leading to a recovery of the exact state set results. Finally, we illustrate the reduction of the overall computational complexity in a decentralized setting by appyling ℓ-complete approximation representation of the distributed state machines.