Construction of Controls Providing the Desired Output of the Linear Stationary Dynamic System

Zubova, S. P.; Raetskaya, E. V.

doi:10.1134/s0005117918050016

Cited by 6 publications

(2 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Equation (28) are sufficient conditions under which inequalities (25) will be fulfilled at t ∈ [0; T]. Now, let us introduce constraints on the state variables of the tracking differentiator (18), its corrective influences, and the rate of their change.…”

Section: Designing a Three-block Tracking Differentiatormentioning

confidence: 99%

“…The signals of the derivatives of the reference influences are usually needed in program control systems [28] as well as when using the feedback linearization method [3]. The order of the required derivatives depends on the number of dynamic links to be considered and is equal to the relative degree of the model used in the control plant.…”

Section: Reasons For Designing Tracking Differentiators With Differen...mentioning

confidence: 99%

See 1 more Smart Citation

Generation of Achievable Three-Dimensional Trajectories for Autonomous Wheeled Vehicles via Tracking Differentiators

Krasnova,

Kokunko,

Kochetkov

et al. 2023

Algorithms

View full text Add to dashboard Cite

Planning an achievable trajectory for a mobile robot usually consists of two steps: (i) finding a path in the form of a sequence of discrete waypoints and (ii) transforming this sequence into a continuous and smooth curve. To solve the second problem, this paper proposes algorithms for automatic dynamic smoothing of the primary path using a tracking differentiator with sigmoid corrective actions. Algorithms for setting the gains of the differentiator are developed, considering a set of design constraints on velocity, acceleration, and jerk for various mobile robots. When tracking a non-smooth primary path, the output variables of the differentiator generate smooth trajectories implemented by a mechanical plant. It is shown that the tracking differentiator with a different number of blocks also generates derivatives of the smoothed trajectory of any required order, taking into account the given constraints. Unlike standard analytical methods of polynomial smoothing, the proposed algorithm has a low computational load. It is easily implemented in real time on the on-board computer. In addition, simple methods for modeling a safety corridor are proposed, taking into account the dimensions of the vehicle when planning a polygon with stationary obstacles. Confirming results of numerical simulation of the developed algorithms are presented.

show abstract

Section: Designing a Three-block Tracking Differentiatormentioning

confidence: 99%

Section: Reasons For Designing Tracking Differentiators With Differen...mentioning

confidence: 99%

Generation of Achievable Three-Dimensional Trajectories for Autonomous Wheeled Vehicles via Tracking Differentiators

Krasnova,

Kokunko,

Kochetkov

et al. 2023

Algorithms

View full text Add to dashboard Cite

show abstract

Solution of the multipoint control problem for a dynamic system in partial derivatives

Zubova

Raetskaya

2020

Math Methods in App Sciences

View full text Add to dashboard Cite

The linear dynamical system in partial derivatives is considered. The system must be transferred from an arbitrary initial state to an arbitrary final state through an arbitrary number of control points. The problem is to find the control for this system. The criterion for the complete controllability of such a system is derived using the method of cascade decomposition. Control and state functions in analytical form are constructed (with any given degree of smoothness), using the method of cascade decomposition.

show abstract

Control Problem for Dynamical Systems with Partial Derivatives

2020

View full text Add to dashboard Cite

Construction of Controls Providing the Desired Output of the Linear Stationary Dynamic System

Cited by 6 publications

References 3 publications

Generation of Achievable Three-Dimensional Trajectories for Autonomous Wheeled Vehicles via Tracking Differentiators

Generation of Achievable Three-Dimensional Trajectories for Autonomous Wheeled Vehicles via Tracking Differentiators

Solution of the multipoint control problem for a dynamic system in partial derivatives

Control Problem for Dynamical Systems with Partial Derivatives

Contact Info

Product

Resources

About