23 research outputs found
Unified Approach to Convex Robust Distributed Control given Arbitrary Information Structures
We consider the problem of computing optimal linear control policies for
linear systems in finite-horizon. The states and the inputs are required to
remain inside pre-specified safety sets at all times despite unknown
disturbances. In this technical note, we focus on the requirement that the
control policy is distributed, in the sense that it can only be based on
partial information about the history of the outputs. It is well-known that
when a condition denoted as Quadratic Invariance (QI) holds, the optimal
distributed control policy can be computed in a tractable way. Our goal is to
unify and generalize the class of information structures over which quadratic
invariance is equivalent to a test over finitely many binary matrices. The test
we propose certifies convexity of the output-feedback distributed control
problem in finite-horizon given any arbitrarily defined information structure,
including the case of time varying communication networks and forgetting
mechanisms. Furthermore, the framework we consider allows for including
polytopic constraints on the states and the inputs in a natural way, without
affecting convexity
Geometric versus Model Predictive Control based guidance algorithms for fixed-wing UAVs in the presence of very strong wind fields.
The recent years have witnessed increased development of small, autonomous fixed-wing Unmanned Aerial Vehicles (UAVs).
In order to unlock widespread applicability of these platforms, they need to be capable of operating under a variety of environmental conditions. Due to their small size, low weight, and low speeds, they require the capability of coping with wind speeds that are approaching or even faster than the nominal airspeed.
In this thesis, a nonlinear-geometric guidance strategy is presented, addressing this problem. More broadly, a methodology is proposed for the high-level control of non-holonomic unicycle-like vehicles in the presence of strong flowfields (e.g. winds, underwater currents) which may outreach the maximum vehicle speed.
The proposed strategy guarantees convergence to a safe and stable vehicle configuration with respect to the flowfield, while preserving some tracking performance with respect to the target path.
As an alternative approach, an algorithm based on Model Predictive Control (MPC) is developed, and a comparison between advantages and disadvantages of both approaches is drawn.
Evaluations in simulations and a challenging real-world flight experiment in very windy conditions confirm the feasibility of the proposed guidance approach
Geometric versus Model Predictive Control based guidance algorithms for fixed-wing UAVs in the presence of very strong wind fields.
The recent years have witnessed increased development of small, autonomous fixed-wing Unmanned Aerial Vehicles (UAVs).
In order to unlock widespread applicability of these platforms, they need to be capable of operating under a variety of environmental conditions. Due to their small size, low weight, and low speeds, they require the capability of coping with wind speeds that are approaching or even faster than the nominal airspeed.
In this thesis, a nonlinear-geometric guidance strategy is presented, addressing this problem. More broadly, a methodology is proposed for the high-level control of non-holonomic unicycle-like vehicles in the presence of strong flowfields (e.g. winds, underwater currents) which may outreach the maximum vehicle speed.
The proposed strategy guarantees convergence to a safe and stable vehicle configuration with respect to the flowfield, while preserving some tracking performance with respect to the target path.
As an alternative approach, an algorithm based on Model Predictive Control (MPC) is developed, and a comparison between advantages and disadvantages of both approaches is drawn.
Evaluations in simulations and a challenging real-world flight experiment in very windy conditions confirm the feasibility of the proposed guidance approach
System-level, Input-output and New Parameterizations of Stabilizing Controllers, and Their Numerical Computation
It is known that the set of internally stabilizing controller
is non-convex, but it admits convex
characterizations using certain closed-loop maps: a classical result is the
{Youla parameterization}, and two recent notions are the {system-level
parameterization} (SLP) and the {input-output parameterization} (IOP). In this
paper, we address the existence of new convex parameterizations and discuss
potential tradeoffs of each parametrization in different scenarios. Our main
contributions are: 1) We first reveal that only four groups of stable
closed-loop transfer matrices are equivalent to internal stability: one of them
is used in the SLP, another one is used in the IOP, and the other two are new,
leading to two new convex parameterizations of . 2)
We then investigate the properties of these parameterizations after imposing
the finite impulse response (FIR) approximation, revealing that the IOP has the
best ability of approximating given FIR
constraints. 3) These four parameterizations require no \emph{a priori}
doubly-coprime factorization of the plant, but impose a set of equality
constraints. However, these equality constraints will never be satisfied
exactly in numerical computation. We prove that the IOP is numerically robust
for open-loop stable plants, in the sense that small mismatches in the equality
constraints do not compromise the closed-loop stability. The SLP is known to
enjoy numerical robustness in the state feedback case; here, we show that
numerical robustness of the four-block SLP controller requires case-by-case
analysis in the general output feedback case.Comment: 20 pages; 5 figures. Added extensions on numerial computation and
robustness of closed-loop parameterization
On the Equivalence of Youla, System-level and Input-output Parameterizations
A convex parameterization of internally stabilizing controllers is
fundamental for many controller synthesis procedures. The celebrated Youla
parameterization relies on a doubly-coprime factorization of the system, while
the recent system-level and input-output characterizations require no
doubly-coprime factorization but a set of equality constraints for achievable
closed-loop responses. In this paper, we present explicit affine mappings among
Youla, system-level and input-output parameterizations. Two direct implications
of the affine mappings are 1) any convex problem in Youla, system level, or
input-output parameters can be equivalently and convexly formulated in any
other one of these frameworks, including the convex system-level synthesis
(SLS); 2) the condition of quadratic invariance (QI) is sufficient and
necessary for the classical distributed control problem to admit an equivalent
convex reformulation in terms of Youla, system-level, or input-output
parameters.Comment: 8 pages, 3 figure
Sparsity Invariance for Convex Design of Distributed Controllers
We address the problem of designing optimal linear time-invariant (LTI)
sparse controllers for LTI systems, which corresponds to minimizing a norm of
the closed-loop system subject to sparsity constraints on the controller
structure. This problem is NP-hard in general and motivates the development of
tractable approximations. We characterize a class of convex restrictions based
on a new notion of Sparsity Invariance (SI). The underlying idea of SI is to
design sparsity patterns for transfer matrices Y(s) and X(s) such that any
corresponding controller K(s)=Y(s)X(s)^-1 exhibits the desired sparsity
pattern. For sparsity constraints, the approach of SI goes beyond the notion of
Quadratic Invariance (QI): 1) the SI approach always yields a convex
restriction; 2) the solution via the SI approach is guaranteed to be globally
optimal when QI holds and performs at least as well as considering a nearest QI
subset. Moreover, the notion of SI naturally applies to designing structured
static controllers, while QI is not utilizable. Numerical examples show that
even for non-QI cases, SI can recover solutions that are 1) globally optimal
and 2) strictly more performing than previous methods
Teoria del consenso e applicazione al problema del coordinamento del moto di robot.
Il sempre crescente numero di applicazioni di reti di sensori, robot cooperanti e formazioni di veicoli, ha fatto sì che le problematiche legate al coordinamento di sistemi multi-agente (MAS) diventassero tra le più studiate nell’ambito della teoria dei controlli.
Esistono numerosi approcci per affrontare il problema, spesso profondamente diversi tra loro. La strategia studiata in questa tesi è basata sulla Teoria del Consenso, che ha una natura distribuita e completamente leader-less; inoltre il contenuto informativo scambiato tra gli agenti è ridotto al minimo.
I primi 3 capitoli introducono ed analizzano le leggi di interazione (Protocolli di Consenso) che permettono di coordinare un Network di sistemi dinamici.
Nel capitolo 4 si pensa all'applicazione della teoria al problema del "loitering" circolare di piĂą robot volanti attorno ad un obiettivo in movimento. Si sviluppa a tale scopo una simulazione in ambiente Matlab/Simulink, che genera le traiettorie di riferimento di raggio e centro impostabili, a partire da qualunque posizione iniziale degli agenti.
Tale simulazione è stata utilizzata presso il “Center for Research on Complex Automated Systems” (CASY-DEI Università di Bologna) per implementare il loitering di una rete di quadrirotori "CrazyFlie". I risultati ed il setup di laboratorio sono riportati nel capitolo 5.
Sviluppi futuri si concentreranno su algoritmi locali che permettano agli agenti di evitare collisioni durante i transitori: il controllo di collision-avoidance dovrĂ essere completamente indipendente da quello di consenso, per non snaturare il protocollo di Consenso stesso