Optimal control using dsolve error

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Praveen Kumar
Praveen Kumar 2019-2-7
回答： Walter Roberson 2019-2-7
Hi,
I am trying to simulate optimal control problem using the method/example provided in Link, but for a different system.. But I am getting following error.
Error using mupadengine/feval (line 187)
Invalid number of arguments.
Error in dsolve>mupadDsolve (line 340)
T = feval(symengine,'symobj::dsolve',sys,x,options);
Error in dsolve (line 194)
sol = mupadDsolve(args, options);
Error in PMP_18012019 (line 35)
sol_h = dsolve(eq1,eq2);
clear;
%Initializations and values of constant variables
C = 28;
Rs = 0.01;
Rp = 10e3;
Vsmax = 305;
Preq = 50e3;
k = 1;
Vb = 360;
Rb = 0.3;
p1 = 0.4;
% State equations
syms x1 Pb p1 z; %Pb control variable & x1 = SOC_s is state variable
Dx1 = -1/C*((1/(2*Rs)+1/Rp)*x1-1/(2*Rs)*sqrt(x1^2-4*Rs/Vsmax^2*(Preq-Pb)));
% Cost function inside integral
syms g;
g = k*((Vb - sqrt(Vb^2 - 4*Rb*Pb))/(2*Rb))^2;
% Hamiltonian
syms p1 H;
H = g + p1*Dx1;
% Costate equations
% Dx1 = diff(H,p1);
Dp1 = -diff(H,x1);
% Solve for control Pb
dPb = diff(H,Pb);
sol_Pb = solve(dPb,Pb);
% Substitute Pb to state equations
Dx1 = subs(Dx1,Pb,sol_Pb);
% Convert symbolic objects to strings for using 'dsolve'
eq1 = strcat('Dx1=',char(Dx1));
eq2 = strcat('Dp1=',char(Dp1));
% consA1 = 'Dx1(0)=0';
% consA2 = 'Dp(0) = 0 ';
sol_h = dsolve(eq1,eq2);
% Use boundary conditions to determine the coefficients
% Case a: (a)Dx1(0)=90 Dx1(tf)=50
conA1 = 'x1(0) = 0';
conA2 = 'x1(10) = 1';
sol_a = dsolve(eq1,eq2,conA1,conA2);
% plot solutions
figure(1)
ezplot(sol_a.x1,[0 1]); hold on;
ezplot(sol_a.p1,[0 1]); % plot the control u=-p1
axis([0 20 0 1]);
xlabel('time');
ylabel('states');
title('Solution of PMP')
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Stephan
Stephan 2019-2-7
编辑：Stephan 2019-2-7
sol_h = dsolve([eq1,eq2]);
...
sol_a = dsolve([eq1,eq2],[conA1,conA2]);
Praveen Kumar
Praveen Kumar 2019-2-7
Made the above changes. Following error is displayed:
Error using symengine
Unexpected 'identifier'.
Error in mupadengine/evalin (line 132)
res = mupadmex(statement,output_type{:});
Error in dsolve>mupadDsolve (line 339)
sys = [sys_sym reshape(evalin(symengine, sys_str), 1, [])];
Error in dsolve (line 194)
sol = mupadDsolve(args, options);
Error in PMP_18012019 (line 37)
sol_h = dsolve([eq1,eq2]);

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回答（1 个）

Walter Roberson
Walter Roberson 2019-2-7
r2018a does not permit dsolve of systems expressed as character vectors and so is thinking those are option names. You need to rewrite into symbolic expressions and
syms x1(t)
dx1 = diff(x1)
dsolve(dx1 == DX1)
or as appropriate .

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