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System Identification and Control Functionality in JULIA

Cristian R. Rojas, Arda Aytekin and Niklas Everitt

Department of Automatic Control,

KTH Royal Institute of Technology

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Background

  • Good software is essential for building engineering applications
  • Currently MATLAB is our main platform for education, research and industrial use in automatic control
  • Great variety of toolboxes for control, signal processing, identification, statistics, power systems, ...

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Drawbacks

  • Expensive
  • Many toolboxes with closed-source code
  • Black-box GUIs hiding details
  • Limited group of contributors
  • Sometimes slow ...

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A Recent Alternative: JULIA

  • Free and open source
  • High-level language (like MATLAB, Python)
  • Yet, high performance (like C, FORTRAN)
  • Ability to generate low-level code for embedding (via LLVM)
  • Fast growing ecosystem of libraries
  • Already adopted for classroom teaching at MIT, Stanford, Cornell, ...

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Did We Mention FAST?

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However ...

  • Until recently (2015), (almost) no support for control and system identification

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Ultimate Goal

  • Provide a free, open and extensible ecosystem of packages

  • For Users: Simple to read, transparent and well-documented, and

  • For Developers: Compact, modular and easy to maintain

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More Specifically ...

  • Basic data types: Different LTI representations and their interactions (ControlCore.jl)
  • Interfaces and contracts for compatiblity among packages (ControlCore.jl)
  • Basic estimation functionality (IdentificationToolbox.jl)
  • Basic analysis and design functionality (ControlToolbox.jl)
  • ... maybe some more (MPCToolbox.jl)?

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ControlCore.jl

  • Learn from mature packages such as MathProgBase.jl, LearnBase.jl, ...

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Basic Data Types

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Parametric Types

  • Needed for efficient, compact and flexible representations
immutable StateSpace{T,S,M<:AbstractMatrix} <: LtiSystem{T,S}
  A::M
  # some more definitions of variables
  # some constructor functions
  # ...
end

# Dense matrices
julia> A1  = eye(N,N); B1 = randn(N,M); C1 = randn(P,N); D1 = randn(P,M);
julia> ss1 = StateSpace(A1,B1,C1,D1);

# Sparse representations
julia> A2  = speye(N,N); B2 = randn(N,M); C2 = randn(P,N); D2 = randn(P,M);
julia> ss2 = StateSpace(A2,B2,C2,D2);

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Parametric Types

  • Also allows for efficient low-level code generation
julia> f(x::Number, y::Number) = x+y
f (generic function with 1 method)

julia> @code_llvm f(1., 2.)

define double @julia_f_70581(double, double) #0 {
top:
  %2 = fadd double %0, %1
    ret double %2
}

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Interfaces and Contracts

  • A set of interface functions needed for inter-operability
# at ControlCore.jl
# enforce existence of `poles(sys::LtiSystem)`

# From ControlToolbox.jl perspective
function isstable{T}(sys::ControlCore.LtiSystem{T,Discrete{true}})
  return all(abs(poles(sys)) .< 1.)
end

function isstable{T}(sys::ControlCore.LtiSystem{T,Discrete{false}})
  return all(real(poles(sys)) .< 0.)
end

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Interfaces and Contracts

# From SystemIdentification.jl perspective
immutable IdType{T,S,U} <: ControlCore.LtiSystem{T,S}
  sys::U
  # some variables specific to the identification method
end

function poles(sys::IdType)
  # implement to obtain poles of the system
end

# `isstable(sys::IdType)` will simply work

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IdentificationToolbox.jl

Current Status

  • Hessian based search (PEM)
  • Instrumental variables (IV4), and
  • Subspace method (N4SID)

Open Issues

  • Standardization (separate interface from implementation),
  • Other approaches such as frequency domain methods, ...

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ControlToolbox.jl

Current Status

  • lsim: step, impulse
  • rlocus, and
  • discretization

Note: Needs re-structuring and some more work.

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Thanks!