We show that a partition of the navigation space can be obtained using convex liftings, providing the means to generate a path from the current to a final position. The feasible domain is efficiently described using zonotopes which have a complexity advantage w. This work treats the zonotopic approximations from a control perspective, providing a set of conditions able to safeguard the initial domain topology. An adaptation of the generic collision avoidance problem is considered, aiming to guarantee the feasibility and highlighting through simulations the advantages offered by the zonotopic representation.
The motivation is to optimize the input value and the next communication instant between the sensor and controller to improve the control performance.
The basic idea is to consider a set of candidate scheduling sequences and solve for each of this sequence a convex, robust optimal control problem based on the state estimate. The best scheduling sequence and the corresponding optimal input are used to schedule the communication and to provide the feedback to the plant. Conditions to guarantee robustly constraint satisfaction,recursive feasibility and robust stability are provided. The approach is illustrated by a simulation example. The vapor compression system uses a variable speed compressor and a set of expansion valves for control, and it is required to regulate zone temperatures to set-points without offset.
Constraints are imposed on all control inputs and also the values of both measured and unmeasured system outputs. Because experimental testing is both expensive and time-consuming, we have developed a tool chain for software-in-the-loop validation that uses a Modelica model for the plant, integrated with a software representation of the MPC that is realized in a combination of Modelica and C that is suitable for real-time use. We show the results of closed-loop tests of the controller with a nonlinear system model, which provide a partial validation of the controller and tool chain.
The cost function of the underlying optimization problem consists of convex stage costs as well as Bregman distances centered around the a priori estimates. The Bregman term allows to incorporate constraints into the cost function by means of relaxed barrier functions and to formulate the moving horizon estimator as an unconstrained optimization problem. The stability properties of the proposed estimator are investigated and the obtained results are illustrated by means of a numerical example.
The low-level MPC makes use of an equivalent hydraulic model EHM that captures the dynamics of relevant internal electro-chemical states.
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This controller calculates the optimal charging current that satisfies the constraints associated with side reactions in anode and cathode. The high-level MPC solves a temperature feasibility problem using a battery thermal model by setting boundaries on the square of the current defined by the low-level control in the previous step. Information is exchanged between layers until the current proposed by low-level controller is feasible for the high-level controller requirements. Simulation results of the aforementioned scheme are compared with an alternative case in which the lower layer predictor uses an equivalent circuit model ECM.
We show that for the same thermal model and tuning parameters, similar performance regarding constraints satisfaction and convergence of the solution for the control action can be obtained for the EHM and ECM. Finally, the distributed approach is compared to a single MPC in which the temperature constraint is enforced by resorting to the thermal equilibrium current, which is calculated off-line.
The latter achieves similar results to the reference case at lower computational cost. Each of the secondary sensors is assigned to a sector of the operation area; a secondary sensor decides which target in its assigned sector to be identified and controls itself to identify the target. We formulate the decision-making process as an optimization problem to minimize the uncertainty of the targets' identities subject to the sensor dynamic constraints.
The proposed algorithm is decentralized since the secondary sensors only communicate with the primary sensor for the target information, and need not to synchronize with each other. By integrating the proposed algorithm with the existing multi-target tracking algorithms, we develop a closed-loop multi-target tracking and identity management algorithm. The effectiveness of the proposed algorithm is demonstrated with illustrative numerical examples.
However, to ensure flight safety, guaranteed consistent uncertainty estimates are of equally crucial importance. Two easily implementable modifications to the Extended Set Membership Filter are shown to greatly reduce its conservatism. The filter runs in fixed time and handles asynchronous observations. As another novelty, we take into account parametric uncertainty of the observation equation.
The proposed filter is applied to a two unmanned aircraft systems UAS localization problem in simulation, with observation noise obtained from real sensors. We compare the new filter to a computationally very strong but much more expensive nonlinear set inversion algorithm and find that similar performances can be achieved. Also, simulation results illustrate the effective reduction of filter conservatism by a small number of iterative updates.
The design is based on a decomposition into locally observable and unobservable substates and on properties of homogeneous systems. Each observer node can reconstruct in finite-time its locally observable substate with its measurements only. Then exploiting the coupling, a finite-time converging observer is constructed for the remaining states by adding the consensus terms.
A numerical example illustrates the result. In doing so, the system can be split into smaller subsystems that can be estimated and controlled more easily. While current state-of-the-art fusion methods for distributed estimation assume the fusion of estimates referring to the full dimension of the state, little effort has been made to account for the fusion of unequal state vectors referring to smaller subsystems of the full system. In this paper, a novel method to fuse overlapping state vectors using a deterministic sample-based fusion method is proposed.
These deterministic samples can be used to account for the correlated and uncorrelated noise terms and are therefore able to reconstruct the joint covariance matrix in a distributed fashion. The performance of the proposed fusion method is compared to other state-of-the-art methods. Moving horizon estimation involves solving a quadratic program to minimize the estimation error relative to a model over a fixed window of past input-output observations.
By exploiting the spatial structure of a chain, two algorithms for solving this quadratic program are considered. Both algorithms can be distributed in the sense that the computations associated with each sub-system component of the state depend only on information associated with the immediate neighbours.
The algorithms differ in the way that the linear Karush-Kuhn-Tucker conditions for optimality are solved. Computational and information dependency overheads are analyzed.https://gurgmebusccomp.tk
Numerical results are presented for a 1-D mass-spring-damper chain. Inspired by the alternate attitude and position distributed optimization framework discussed in , we propose an estimation scheme that exploits the unit dual quaternion algebra to describe the sensors pose. This representation is beneficial in the formulation of the optimization scheme in that it allows to solve the localization problem without designing two interlaced position and orientation estimators, thus improving the estimation error distribution over the two pose components and the overall localization performance.
Furthermore, the numerical experimentation asserts the robustness of the proposed algorithm w. Standard feedforward methods to achieve these goals are inversion-based feedforward control and input shaping.
The former achieves perfect tracking but lacks robustness to uncertainties in the system dynamics while the latter may account for robustness at the expense of reduced tracking performance. In this work, a continuous time finite-impulse-response FIR prefilter design for linear systems is proposed which allows to trade off tracking performance against robustness. The approach is based on a finite time linear quadratic LQ optimal control formulation of the filtering task.
Robustness is taken into account by penalizing large magnitudes of the trajectory sensitivity. Tracking delay can be reduced by adjusting the filter length which is a free design parameter. With the proposed prefiltering scheme fast and robust tracking can be achieved. An important application is simultaneous tracking and vibration suppression for motion systems with uncertain elasticity parameters which is used as a simulation example.
The special case where the unknown inputs have direct feedthrough to the outputs is considered. Necessary and sufficient conditions are given under which an unbiased pseudo state and input estimation is possible. The prediction step of the fractional Kalman filter uses an approximation as it can not be calculated exactly in practice. Therefore, the estimation procedure is suboptimal. Nevertheless, the method yields accurate estimates of pseudo states and unknown inputs which is illustrated by means of an academic example.
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By sending a sample only when some triggering condition is fulfilled, we can ensure that the transmitted samples actually carry innovation. However, in an event-based system, the state estimation problem becomes complicated, as the information of not receiving a measurement must be taken into consideration. Recent research has examined the feasibility of using particle filters for solving the event-based state estimation problem.
To the best of our knowledge, only the simple bootstrap particle filter has so far been considered in this setting. We argue that, as this filter does not fully utilize the current measurement, it is not well suited for state estimation in event-based systems. We propose an extension to the auxiliary particle filter for systems with event-based measurements, in which certain existing techniques for finding an approximation of the fully adapted filter can easily be utilized.
In a simulation study, we demonstrate that at new measurement events, the benefits of using the auxiliary particle filter increases when fewer measurements are being sent. The algorithm uses numerically stable square-root formulas, can handle simultaneous independent measurements and non-equally spaced abscissas, and can compute state estimates at points between the data abscissas. The state space model's parameters, including driving noise intensity, measurement variance, and initial state, are determined from the given data sequence using maximum likelihood estimation computed using an expectation maximisation iteration.
In tests with synthetic biomechanics data, the algorithm is found to be more accurate compared to a widely used open source automatic numerical differentiation algorithm, especially for acceleration estimation. However, sometimes the dynamical system evolves in such a way that online learning is preferable.
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