Abstract A fundamental quantity of the solution of an optimal control problem is the value function, i.e., the optimal cost-to-go function. In the general case, the function is not known exactly, but need to be approx...
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Abstract A fundamental quantity of the solution of an optimal control problem is the value function, i.e., the optimal cost-to-go function. In the general case, the function is not known exactly, but need to be approximated numerically. Most approaches to numerical approximation of the value function follow a procedure of three steps: first, the original continuous problem formulation is fully discretized; second, the discretized finite optimal control problem is solved by a shortest-path algorithm, and as third step, the solution is projected back from the finite space onto the continuous state space by using an interpolating function. This paper investigates the differences of discretization schemes and interpolating functions in this context. The performance of the computed approximations is evaluated in terms of an a-posteriori error, which is obtained from the approximating value functions. The convergence of the approximations to the true value function is proved for all considered schemes for the case that the discretization parameters are decreased to zero.
The applications of two typical swarm intelligence algorithms in the optimization of the reentry trajectory for the hypersonic gliding vehicles are discussed in our paper. A trajectory optimization strategy based on t...
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Abstract The distributed Maxwell-slip model provides a convenient way to describe the presliding friction behavior. The modified single-state Maxwell-slip (MMS) model is proposed with the main benefit to require two c...
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Abstract The distributed Maxwell-slip model provides a convenient way to describe the presliding friction behavior. The modified single-state Maxwell-slip (MMS) model is proposed with the main benefit to require two concentrated parameters only when describing the smooth hysteresis of the presliding friction. The model is rate-independent at both, saturated and unsaturated hysteresis, and is consistent with the generalized empirical friction model structure. Some novel perceptions on the frictional memory and drift are considered and proved in experiments. The evaluation performed on an actuator system with multiple coupled frictional surfaces reveals the proposed model as easily identifiable and accurate in prediction.
Abstract In this paper, the extended state dependent Riccati equation (ESDRE) method is applied to robotic joint control. The control scheme compares the predicted reference state and the actual state, thus rapidly re...
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Abstract In this paper, the extended state dependent Riccati equation (ESDRE) method is applied to robotic joint control. The control scheme compares the predicted reference state and the actual state, thus rapidly reducing the steady-state error, even in the presence of significant model uncertainties. The state dependent coefficient (SDC) model and the corresponding control law are formulated for the discrete state-space by linear interpolation among operating points. The approach is validated on a 1-DOF rigid robotic manipulator which major nonlinearities are the velocity dependent Stribeck friction and the position dependent gravity. Considering the relative weighting matrices as parameters of the underlying optimization problem by control design the state dependent feedback function is determined. The developed ESDRE control proves superior compared to the PID reference controller with auxiliary gravity compensator. Considering the robust performance and ease of implementation the proposed ESDRE scheme constitutes a serious competitor to the established model-based robot control strategies.
In this paper we propose a novel distributed algorithm to solve degenerate linear programs on asynchronous networks. Namely, we propose a distributed version of the well known simplex algorithm. We prove its convergen...
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Identification of dynamic friction is precursory to the friction compensation in the motion control systems. This paper discusses and proves experimentally the FRF based identification of dynamic friction described by...
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Identification of dynamic friction is precursory to the friction compensation in the motion control systems. This paper discusses and proves experimentally the FRF based identification of dynamic friction described by means of the recently developed two-state friction model with elasto-plasticity. The frequency-domain friction characteristics are analyzed using a quite simple excitation which however discloses both, the presliding and sliding regimes. Most importantly, the proposed friction identification, which is nowadays rarely performed in frequency-domain, offers an adequate model accuracy validated in time-domain on the unseen velocity response data.
Modeling and identification of dynamic systems often is a prerequisite for the engineering of technical solutions, for example control system design. This paper presents an multi objective evolutionary approach for id...
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Modeling and identification of dynamic systems often is a prerequisite for the engineering of technical solutions, for example control system design. This paper presents an multi objective evolutionary approach for identification of dynamic systems of variable structure. The evolutionary algorithm employs domain specific operators in order to evolve the block oriented structure of the model and simultaneously optimize its parameters. Based on the observed inputs and outputs the multi objective method identifies an entire set of optimal compromise models which contrast model accuracy against complexity. The models are constructed from a set of basic blocks that capture phenomenons such as linear transfer functions, nonlinear gains and hysteresis that typically occur in mechanical, hydraulic and electrical systems. This representation enables the incorporation of domain knowledge in terms of building blocks and the interpretation of the identified model for further analysis and design. The feasibility of the proposed method is validated in the identification of an artificial dynamic system as well as a hydraulic proportional valve.
Abstract In this paper, the average consensus problem for multi-agent systems is addressed. A novel event-based control strategy is proposed which renders both control signals and state measurements, which are broadca...
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Abstract In this paper, the average consensus problem for multi-agent systems is addressed. A novel event-based control strategy is proposed which renders both control signals and state measurements, which are broadcast over the network, piecewise constant. This enables implementation on digital platforms such as microprocessors. Different triggering conditions guaranteeing convergence to an adjustable region around the average consensus point or asymptotic convergence to this point, respectively, are discussed. Numerical simulations show the effectiveness of this approach, outperforming traditional time-scheduled control in terms of load on the communication medium. Both single- and double-integrator agents are covered.
Abstract We consider inherent robustness properties of model predictive control (MPC) for continuous-time nonlinear systems with input constraints and terminal constraints. We show that when the linear quadratic contr...
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Abstract We consider inherent robustness properties of model predictive control (MPC) for continuous-time nonlinear systems with input constraints and terminal constraints. We show that when the linear quadratic control law is chosen as the terminal control law, and the related Lyapunov matrix is chosen as the terminal penalty matrix, MPC with nominal prediction model and bounded disturbances has some degree of inherent robustness. We emphasize that the input constraint sets can be any compact set rather than convex sets, and our results do not rely on the continuity of the optimal cost functional or control law in the interior of the feasible region.
Abstract We consider an optimal control problem for networked control systems, where the loop is closed via a lossy, distributed network with an acknowledgment mechanism. The network is distributed in the sense that t...
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Abstract We consider an optimal control problem for networked control systems, where the loop is closed via a lossy, distributed network with an acknowledgment mechanism. The network is distributed in the sense that there are different sets of sensors and actuators that each communicate individually with the controller. We assume that all packets, i.e., the measurement packets, the control packets and the acknowledgment packets are sent over the lossy network and thus are subject to loss. We derive suboptimal controllers with respect to a quadratic cost criterion for the general case and optimal controllers for the case that all states are perfectly measured over a single link. Additionally, we present stability criteria for both cases.
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