Advanced Control Strategies for the Robotic Hand

Rotational Motion Control by Feedback with Minimum L1-Norm

The control design for the Cobra maneuver of quadrotors is presented based on quaternion dynamics. Cobra maneuver commands the quadrotor in ± π / 2 (rad) pitch angle such that the conventional hovering assumption for quadrotor flight is not applicable. The finite-time θ-D method is proposed to control the Cobra maneuver. Based on this technique, the intractable Hamilton–Jacobi–Bellman equation can be approximated by a differential Riccati equation and a series of state-dependent Lyapunov equations, which can be solved recursively and lead to the closed-form state feedback control law . This control law can achieve semi-global asymptomatic stability of the closed-loop system. Numerical simulations verify that the proposed technique is compared favourably with the finite-time state-dependent Riccati equation (SDRE) technique in terms of computation efficiency and control effort, and also shows faster recovery of the quadrotor after the Cobra maneuver compared with conventional dynamics without the derivative of the rotation matrix.

We are concerned with difference Riccati equations in the complex plane. We study the continuous limit of difference Riccati equations to differential Riccati equations, and compare asymptotic expansions of both of solutions. Some examples are constructed. We also consider ramification relations and value distributions of transcendental meromorphic solutions to difference Riccati equations.

This paper proposes the solution of state-dependent Riccati equation as a nonlinear optimal regulator to stabilise the motion dynamics of the vehicle model subjected to sudden disturbance inputs in the lateral direction. The proposed nonlinear regulator coordinates individually actuated wheel braking torque and steering wheel angle simultaneously in an optimal manner. Performance criteria are satisfied by solving the Riccati equation based on the given cost function subjected to the nonlinear vehicle dynamics. On-line control allocation in terms of optimal brake torque distribution enhanced by optimal wheel steering angle input is achieved. Furthermore, the proposed optimal nonlinear regulator is an active fault-tolerant control system against partial by-wire actuator failures while guaranteeing stability with good performance due to its capability to allocate the individual control inputs in an optimal way. The main aim is to stabilise the motion dynamics of the vehicle model during short-term emergency situations along the desired straight trajectory manageable by average drivers and to provide vehicle stability and handling predictability through the interaction of individual wheel braking and steering actuators. Simulation results are used to illustrate the effectiveness of the proposed methodology.

Analytical representation of the state-dependent coefficients in the SDRE/SDDRE scheme for multivariable systems

Max-plus representation for the fundamental solution of the time-varying differential Riccati equation

A closed-form feedback solution to finite-time optimal control problems for input-affine non-linear systems is presented here. Based on the state-dependent Riccati equation (SDRE) framework, this suboptimal solution, called balanced-cost SDRE (BCSDRE), is proposed to minimise the overall control effort required for driving the system from an arbitrary initial condition to an acceptable neighbourhood around origin, within a pre-specified final time. The state error is dynamically penalised to balance the overall state error and the control cost, resulting in a modified SDRE. Unlike the existing finite-horizon SDRE methods, the proposed technique does not require to solve algebraic Riccati and Lyapunov equations at every time step, which makes this approach computationally efficient. Based on the Lyapunov theory, the origin of the BCSDRE controlled system is shown to be locally exponentially stable. Furthermore, the state profile is also shown to be locally predefined time ultimately bounded, under appropriate tuning of the proposed controller. The proposed technique is implemented to design a controller for the Van der Pol oscillator and impact angle guidance design problem, and its performance is compared with the existing finite-horizon SDRE-based techniques.

The standard H/sub /spl infin// problem is solved for LTI systems with a single, pure input lag. The solution is based on state-space analysis, mixing a finite-dimensional and an abstract evolution model. Utilizing the relatively simple structure of these distributed systems, the associated operator Riccati equations are reduced to a combination of two algebraic Riccati equations and one differential Riccati equation over the delay interval. The results easily extend to finite time and time-varying problems where the algebraic Riccati equations are substituted by differential Riccati equations over the process time duration.

We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the field of optimal control. In order to approximate their solution, one may use several different kinds of numerical methods. Of these, splitting schemes are often a very competitive choice. In this article, we investigate the use of graphical processing units (GPUs) to parallelize such schemes and thereby further increase their effectiveness. According to our numerical experiments, large speed-ups are often observed for sufficiently large matrices. We also provide a comparison between different splitting strategies, demonstrating that splitting the equations into a moderate number of subproblems is generally optimal.

Permanent Magnet Synchronous Motors (PMSMs) are prevalent today due to their advantages, including high efficiency and power. They are the primary motor in most Electric Vehicles (EVs), providing precise, rapid movements for industrial robots and CNC machines, and they act as generators in wind turbines. Therefore, identifying them and designing efficient controllers are crucial, resulting in higher performance and benefiting their capacities. According to the nonlinearities of the PMSM mathematical model and its sensitivity to external disturbances, designing a controller for this type of motor is challenging, and it degrades the performance of conventional linear controllers such as PI controllers. To address this problem, this paper evaluates the performance of an integrated control strategy that combines an advanced suboptimal tracker with an Extended Kalman Filter (EKF). The controller is based on a novel State-Dependent Riccati Equation (SDRE) technique that overcomes the limitations of traditional SDRE regulators by transforming the tracking problem into an equivalent regulation problem. Applying this unique formulation, the tracking of non-decaying reference trajectories will be possible using a discounted cost function, and controller gains are generated from a single Riccati equation. This methodology avoids the need to solve the complex Hamilton-Jacobi-Bellman equation. Concurrently, the EKF can estimate the unknown load torque online and is designed to reject disturbances proactively. Combining EKF and the novel SDRE method results in a nonlinear control structure that enhances tracking accuracy and system robustness.

Theoretical Study of the Nonlinear Control Algorithms with Continuous and Discrete-Time State Dependent Riccati Equation

On the benefits of the [formula omitted] factorization for large-scale differential matrix equation solvers

An adaptive method with weight matrix as a function of the state to design the rotatory flexible system control law

Generalized partitioned solutions of Riccati equations are presented in terms of forward and backward-time differentiations that are theoretically interesting, computationally attractive, as well as they provide important new interpretations of these results. This approach leads also to important generalizations of previous Riccati solutions such as the Chandrasekhar and the partitioned algorithms. Specifically, it is shown that the generalized partitioned solutions may be given in terms of a generalized Chandrasekhar algorithm. These generalizations pertain to arbitrary initial conditions and time-varying models. Furthermore, based on these partitioned solutions, robust and fast algorithms are obtained for the effective numerical solution of Riccati equations. A particularly effective doubling algorithm is also given for calculating the steady-state solution of time-invariant Riccati equations. The partitioned algorithms are given exactly in terms of a set of elemental solutions which are both simple as well as completely decoupled, and as such computable in either a parallel or serial processing mode. Moreover, the overall solution is given by a simple recursive operation on the elemental solutions.

The scattering formulation characterising the effects of and waves in a physical flow process which includes a series of is discussed. Similar concepts can be applied in the linear optimal control problem which includes terminal constraints and the defining linear and quadratic matrix differential equations are shown to be analogous in both cases. The control problem is also shown to include a series of obstacles which can be interconnected according to the properties of the star product which forms the basis of the scattering representation of the general physical system. The scattering matrix of electrical network theory and the associated power relations are also shown to exist analogously in the linear optimal regulator problem. The resulting incident and reflected variables possess similar properties to the scattering variables of network theory and the particular form of scattering matrix is shown to be closely related to the matrix solution of the steady-state Riccati equation. More general energy considerations are extended to the optimal control problem and discussed in terms of inequality properties of a scattering-type matrix and a particular solution of the Riccati equation is shown to be associated with the property defining the state of dissipation in the physical system.